Wednesday's SMG
Her SMG is buffed by all the things that you'd expect it to be buffed by - ATK, ballistic damage buffs, Electrical damage buffs, etc. ... Her SMG works exactly as you'd expect.
Raven Drones
All of Wednesdays drones can of course make full use of the extra damage gained from debuffing enemies DEF and Resistances, as expected.
Similarly, all Auxiliary Unit buffs always affect them.
Wednesday's passive causes her to summon a drone that is always with her.
Since this drone has unlimited duration and can't be destroyed, it's always there, and that means it inherits Wednesdays ATK at the start of the fight and then its stats never change - it's ATK is always 100% of what Wednesday's ATK was when the fight started.
Wednesdays Standard Skill causes her to summon 2 or 4 more drones (depending on if you have her Neuronics or not).
These inherit the ATK stat that Wednesday has at the time the drones are summoned.
This means that they will benefit from other ATK buffs that Wednesday has at the time that they are summoned.
This mean they will always deal equal to or more damage than the regular passive drone.
This means that ATK buffs benefit Wednesday more than other types of buff (electrical, ballistic), as the summoned drones can inherit Wednesday's ATK buffs.
Similarly, if you never bother to summon any extra drones, then since the passive drone is unaffected by any other buffs, you can just ignored buffing the drones ATK entirely.
Beyond that, the buffs the drones receive are extremely eclectic, benefitting from a small number of other buffs
These generally make some sense when you think about them:
Riptide's M2 Skill DMG buff doesn't affect the drones
+Skill DMG only buffs damage from the skill, but Lyfe's skill doesn't deal damage with the drones, it merely creates the drones who then deal their own damage.
Celestial Swans Nebula squads "increases all types of DMG of full squad" buff can apply to them.
The Ravens are a part of Wednesdays damage, and hence should count for this, as Vidya buffs everything.
Celestial Swans 4* weapon Gearlock's "increases all types of DMG of full squad" buff does not persist for them.
This is a buff provided by Vidya, so when Vidya stops providing it, Wednesday (and by extension her drones) also stop receiving it.
I haven't tried every buff in the game to see if it works with the drones, and I have no intention of doing so, but just know that the things that affect the drones are extremely scarce, and other than ATK buffs basically nothing actually buffs them.
Similarly, also note that everything that does affect the drones also affects Wednesday herself, with the one exception of Auxiliary Unit Strength.
In addition, if Wednesday gains an ATK buff, it only affects the drones if she summons the drones whilst she has the buff - if Wednesday doesn't have a buff when she summons the drones, then they don't get it, meaning it's possible for Wednesday to have 99% uptime on a certain ATK buff but if she never has it when she summons her drones then her drones will never receive it.
Similarly, if Wednesday summons some drones that have no ATK buffs, then uses her standard skill whilst she has some ATK buffs, the old non-buffed drones will get their duration refreshed rather than being replaced with new drones.
This does mean that you can just buff Wednesday once and then keep her buffed drones up indefinitely ,but it also means that if you summoned weak drones then you may have to avoid using support skills for the remained of their duration to get rid of them.
The TL:DR is that the summoned Ravens can be buffed by Wednesdays ATK buffs, but Wednesday can gain many buffs that don't affect the drones, and the drones themselves can be kinda finicky to use optimally.
Drone Missile Strike
This comes from the drones.
I.e. Wednesday uses the skill, which creates the drones (or refreshes the duration of existing drones, as above), who then use the skill themselves.
This means the drones' Missile Strike scales off of the drones' ATK at the time the skill is used, not Wednesdays.
This means that if any new buffs are gained/lost after using the skill but before the missiles hit, those buffs will not affect the missile damage.
I.e. You can't use the skill, buff yourself or the drones before the missiles hit, and have them deal increased damage.
This also means that since Lyfe is not the one actually using the skill, any buffs Lyfe gets to Skill DMG also do not apply to the missile strike.
(and the same for other types of buff - electrical dmg buffs, standard skill dmg buffs, etc. - nothing applies.)
Since the drones can't inherit any actual buffs from Wednesday, any buffs Wednesday have don't get transferred to the drones, so again - things like electrical or skill dmg buffs can never benefit the drones damage.
Each drone performs its own missile strike, and each drone is independent of every other drone.
This means that the "Each time a missile hits a part that was already hit, DMG dealt decreases by 50%" is done uniquely per drone - one drones hits don't reduce the damage of the other drones. Since the drones can't really get any buffs to DMG dealt, this is essentially functioning as a Final DMG modifier.
The damage of the first missile is 26% of Raven's ATK + 27, and 9 missiles are fired.
Assuming all missiles hit, the total damage inflicted is 51.898% of Raven's ATK + 279.
This means the total damage is about 180% the damage of the first missile hit. [180.429%]
For 4 Ravens this is a total of around 10,458 damage at 4,500 ATK
Wednesday vs Her Drones
The summoned drones inherit Wednesday's ATK at the time of their creation, so 4 of Wednesdays drones also benefit from any ATK buffs you can give them.
Since you can extend the duration of her drones, you can potentially keep her drones with very high ATK for longer than normal.
E.g. If an ATK buff normally has 50% uptime, then you can use if when the drones are created and then keep the drones up, potentially allowing them 100% buff uptime.
Wednesday's drones deal (7.7% of Raven's ATK + 7) each, and each drone shoots around once per second.
Since you can maintain 100% uptime on all 5 drones, this means that her drones are doing ( 7.7% + 7 )*5 = (38.5% ATK + 35) damage per second.
AT 4,500 ATK this is 353.5 dps per drone, or 1,767.5 dps total over 5 drones.
Factoring in the extra RoF the drones get from Wednesday's M2 bonus, this is increased by 33.27%, up to 2,355.54 dps
(This will be slightly less in practice as Wednesday has to stop shooting to use her skills, as well as Wednesday missing her shots which reduces her M2 bonus.)
The missiles do an extra (51.9%+279) every 25s, for each of the 4 summoned drones.
Over the 25 second cooldown this averages 101.57 dps per raven, for a total dps for the 4 ravens of 418.3 dps.
If Wednesday is at M5, each shot from her drones have a 30% chance to also deal 15% of their ATK as a Whispering Arrow.
Assuming Wednesday is dealing weakspot damage every 5s to proc her M3 bonus too, this means each drone is doing one Whispering Arrow every 2s, for an extra 15 /s
15% /s is an extra 675 dps, per Raven, which is an extra 3,375 dps for all 5 Ravens.
In total, this adds up to 2,355.54 + 418.3 + 3,375 = 6,148.84 dps
Again, this is increased by ATK as well as Auxiliary Unit Bonus.
Her Aux unit buffs would be her Usha 2/3 bonus (24%), her Usha 3/3 bonus (42%), Deiwos (36%), logistics (31.8%), and her Alignment Index (30.9% at 618 Alignment Index).
This totals 164.7%.
This means that for a 4,500 ATK Wednesday, her drones have a max theoretical damage (excluding ATK buffs) of 16,275.97
Assuming Wednesday has around 4,500 ATK, then factoring in Compatibility, Ammo Capacity, RoF, and Reload Speed for a max-level Work-in-Progress, then a 4,500 ATK Wednesday is going to be dealing around 14,734 dps just from the bullets from her Work-in-Progress.
This means that even at absolutely maximum investment and under perfect conditions, her drones deal roughly the same damage as Wednesday deals whilst Wednesday is completely unbuffed.
A completely unbuffed Wednesday shooting at an enemy weakspot deals around 17.6% more damage than her drones do with max investment and under perfect conditions.
Even adding in some relatively minor buffs for Wednesday causes her to out-damage her drones by a notable amount.
Wednesday will of course also be buffed by ATK buffs as well, but she also gains damage from her crits as well as from ballistic dmg, electrical dmg, and aptitude buffs.
So, is it ever actually worth it to invest into Wednesday's drones?
In a vacuum - no. Wednesday deals so much more damage than her drones that even a minor buff for Wednesday is worth more than a major buff for her drones.
(Usha squad adds 66% to her drones. To get the same damage increase to her SMG's damage, Wednesday herself would only need a 27.5% increase in a worst-case scenario.)
Outside of a vacuum - Wednesday is one of your teams three operatives.
If you are using her drones then Wednesday is your dps operative, meaning she has two support operatives to buff her damage.
Whilst there are many support operatives that provide only ATK buffs (and thus buff her drones and herself equally), for most support operatives they provide many buffs, all of which can benefit Wednesday, but only some of which (I.e. the ATK) buff her drones.
This means that almost all support operatives provide a larger damage buff to Wednesday than they do to her drones.
Given that even some of the support abilities you gain access to very early in the game can buff Wednesday quite a lot, there is no scenario where investing into Wednesday's drones provides a larger dps increase than investing into the dps of Wednesday's SMG.Â
TL:DR (Again): Wednesday's drones are terrible, and you shouldn't invest into them.