pretty much everything Enla said, this fight is actually really sch friendly in that if the party is aware of mechanics the sch mwont have much healing to do aside from the occasional tank busters and ukehi (probably butchered that name lol) AOE's. but this is where I find most use of a few of our skills.
Adlo - as always use it to shield the tank from incoming busters, you really shouldn't be required to do any other healing on the tank tbh depending on your group and co healer.
succor- pop one before the multiple AOE's start and everyone should be fine (do not spam this move, you WILL burn mana)
Indom- useful during sword phase after the second break, pop it to help bring the party back to full health before the incoming big damage. also use as an emergency heal if to much damage is being taken during ukehi or if partner healer is dead.
sacred soil - not required but more mitigation during uheki is never a bad thing and its very easy to have soil up as you will get a rhythm for when uheki is coming again.
Fairy- whispering dawn is helpful and when combined with succor at the beginning of sword phase can ease a bit of the strain during sword phase on your partner healer while you focus the OT.
Fey union - sadly useless ignore your fairy gauge in this fight
physick- your go to band aid heal as always spam on the OT during sword, if he dips to low and is in danger of being killed by the next orb throw a lustrate at him but honestly physick should be enough.
these are pretty much the only healing skills I HAVE to use during this fight, I opt out of some depending on the situation and my party, co healer, and tanks. So you may wonder what do sch do in the time we are not healing (which is 80% of the time) the answer is DPS!
that's it if your group is handling mechanics and your main healer is healing you should be spending most of your time doing as much dps as you can.