I'm going to have to insist that all Blue Lily actions remain heals. We already have trouble valuing them properly as is, adding a damage option that still builds Blood Lily buries the entire system.
But this is a scholar thread so -
I've never liked the pet. There's not been an iteration of it that hasn't annoyed me in some manner, and the continued issues with Scholar and Summoner have only steered me more to "Get rid of them" over the years. So if we're just throwing out what we'd like to see...
As a rough and basic overview, I'd like to see Eos/Selene become passengers rather than be their own entities. They have two basic functions they heed.
A) Follow. Orders a Faerie to attach to a target. By default they are on the scholar's shoulder. Eos provides whoever she's 'following' Embrace, a HoT effect. Selene provides whatever Enemy she's attached to a DoT effect, and will move to the nearest aggro'ed enemy should the current be defeated.
B) Set. Places the Faerie at target location. They extend their default skill to an area at weaker potency. (Eos aoe regens, Selene AoE Dots)
This serves as scholar reimplementation of the old Cleric Stance system. You have Eos out to heal, you have Selene out to deal damage. This also gives us a significant way to improve Dissipation - While the Scholar can swap Faeries by default, Dissipation effectively empowers the opposing Faerie - Locking you out of one for 30s but greatly improving both their, and your, effectiveness.
Example: Eat Eos - Improve your healing capabilities, improve everything sourced from Selene (Usually damage). Eat Selene, improve your damage, improve everything sourced from Eos (Usually healing.)
With this design point in mind, we have a pretty clear goal. We build the Scholar (and faeries) around separate and limited damage/healing kits. When the Scholar is on the offensive, Eos is out to cover. Once the Scholar's offensive options are extinguished, Selene comes out.
We could enforce this via action swapping based on which Faerie is active, but I imagine old scholar mains would much prefer to treat this more as a 'guideline' than a requirement - If you can get away with Selene out and going offensive, that should be an option, just as the ability to turtle up with Eos should be an option.
The introduction of the Fey gauge and Fey Union we'd take a different approach with. Rather than be limited to two abilities, instead the Fey gauge is drained to allow both Faeries to be active at once. Fey Union becomes a cooldown, causing all active faeries to mimic your GCD actions at the chosen target, as weakened and separate effects.
Seraph is now a temporary summon for 30s / 120recast. She grants the ally she follows a Barrier every 6seconds, or applies it to the area she is set at a weaker potency.