Ultimate Skill
Celestial Swan marks the target as a Prime Suspect.
If that enemies HP gets below a certain amount (determined by Celestial Swan's U-Energy) then Vidya immediately executes them.
(Mechanically, Vidya deals True DMG to the target - meaning it ignores things like DEF and resistances - the target just takes its current HP as damage, thus dying.)
In practice, the HP threshold for this to trigger is so low it's often useless, and it isn't something you want to save your U-Energy for.
Note that Celestial Swans ult has infinite duration - Once marked, an enemy stays marked forever until either Vidya executes them or you use her ult again to mark another target.
Her ult isn't that useful by itself, but it is very useful for proc'ing her M5 Manifestation buff if the target also has Vidya's Support Skill used against them.
With its Neuronic, it also reduces the targets ATK by 10%, which is an ok survivability buff.
It's also useful as it provides an icon above the marked enemy, which can help locate them amidst visual clutter.
As such, you should always immediately use her ultimate skill against the boss a soon as a fight starts against one.
Support Skill
Vidya's Support Skill reduces the targeted enemies DEF, resulting in you dealing a decent amount more damage to them.
In addition, damaging the target causes them to decrease their resistance to the type of damage they took.
This stacks up to 5 times, and the target can gain 1 stack every 2 seconds, however with its Neuronic Vidya can immediately inflict 4 stacks, meaning she can stack the max debuff pretty much instantly.
The DEF debuff is 16%, 28% with M1, or 29.6% with M4.
If Celestial Swan' has M5, then if her support skill is used on the same target as her ult, that target also gains 8% Increased DMG Taken, which is extremely strong.
Each stack of the debuff grants 5% ResPen, for 25% total, or 35% total with M2.
With M3 being at max stacks of the debuff also grant a 15% ATK buff to all other operatives.
With M4 the debuff is increased to 5.5% per stack, for 38.5% total Resistance reduction.
This skill uses S-Energy continuously, and Vidya doesn't recover S-Energy whilst it's active.
It uses 1 S-Energy every 0.2s, for 5/s, meaning it has an uptime of 10 seconds.
This skill has a 5s cooldown after it ends. After the cooldown is over, Vidya recovers 50 S-Energy (which is her max), so she can immediately use it again.
This means this skill has a 10 second duration and a 5 second cooldown, for 66.6% total uptime.
If Vidya has her 5* weapon, then her Support Skill has unlimited duration - it never expires.
Most critically though, is that Celestial Swans Support Skill only provides a damage reduction to one damage type at any given time.
If an enemy is damaged by a new damage type, then it loses its resistance reduction to its previous type.
This means that you can't use multiple different damage types and have Celestial Swan buff all of them.
In practice this means that if you are using Celestial Swan, then you will want your other support operative to either not deal damage, or to deal the same type of damage as your main DPS.
If using Celestial Swan, then having your other support operative and your DPS not type-match is a very significant DPS loss compared to having them type-match, to the extent that if the other support and the dps don't type-match then you're usually better off using another support instead of Celestial Swan, or swapping the other support for a weaker support that does work with Celestial Swan.
This can make teambuilding with Celestial Swan quite complicated, as the main dps will always need to type-match the other support operative.
This also means that some supports work well alongide Celestial Swan simply because they don't deal damage, and thus don't get in the way of Vidya debuffing the damage type of the main DPS. For example Eatchel - The Cub.