We know it'll be Noct Sect on AST, which I am okay with on the condition it means they can resolve our complaints with healers. IMO what needs to be done to get us moving in the right direction:

WHM:
You're nearly there, I mean the healing side flows and works, but it's just so boring. Give it more to do in its downtime. WHM is meant to be the most powerful of the healer jobs as part of it identity (with SCH being tactical and AST being technical), heck maybe use a proc-like system for DPS like Level 50 BLM has and throw in a couple of extra abilities. An example use might be: you have Stone IV and Aero III as your DPS abilities but there's percentage chance that it will proc Tornado or Quake. Tornado can be all of Aero III's damage at once, Quake can be a stronger Stone. Make Dia into a utility spell, maybe a defense debuff on an enemy. Make Glare into a Lily dump like SCH has an aetherflow dump, so people aren't sitting on unused lilies and can get their Afflatus Misery procs more. Tornado and Quake already exist in game and just teasing WHM's whilst BLM has Flare and Freeze.

Doing it this way would keep WHM DPS very simple, but offers more interactive and breaks up Glare spams. It would keep WHM approachable for beginners but give more for veterans to not be bored out of their minds.

SCH:
This is a mess TBH. On the healing side, create more dependence on shields. Shield healing used to be a healing style but with how effective its oGCD's are and the lower healing requirement shields end up being a safety buffer or a niche use and not a healing style. This I feel will be a NECESSITY with the upcoming shield/pure healer divide for it to work. Make SCH a true Shield healer again, it is currently a pure healer with extra shields. Model Sage's balance off of this.
Then give it back its DoT mage identity. DoT Mage always made more sense for SCH than SMN. SMN is in need of a rework, so this is an opportunity to differentiate the two this way & give SMN more pet love/focus. In our DPS kit we should have: Bio, Bio II/Biolysis, Miasma, Miasma II, Bane, Broil, Shadowflare, Energy Drain
Bring back Selene's abilities, give her more utility instead of deleting her. Make more use of faeries.
Think more about how SCH's healing abilities work together. Do we really need Dissipation?


AST:
I think its Diurnal Sect healing is fine.
Sacrificing Noct Sect is fine if it means we'll get a better healer situation. But please don't sacrifice Neutral Sect as part of that.
Bring back the old card system with some adjustments:
- Change card effects to accommodate TP loss - Direct Hit & Crit hit are options.
- Balance healers so MP management is a thing again or give the Ewer a different effect - I feel like The Ewer would now very niche or used for Royal Road. Personally I'd prefer to have MP management again. Even then, potential DRK & PLD benefits.
- Replace Sleeve Draw with Hold
- Replace Divination with Royal Road
- Reduce Redraw charges to 1
- Keep the Current Minor Arcana system
I envisage the following from it:
A Redraw charge reduction will cripple any fishing attempts and reduce card fishing. The current Minor Arcana system offers a beneficial alternative to card fishing, so your fail scenario is still a DPS boost and no card feels wasted. Royal Road could affect card choice. You might use hold to keep cards you don't need now but might need later, eg: The Bole or The Ewer or any you might want to use with Royal Road but lack a Royal Road card at present, eg: The Balance or The Arrow.

General Healing:
Up the healing requirement in non-highend content. I should not be able to do a dungeon run where maybe 20$ or 30% of the abilities I use are healing related. Having better DPS abilities would at least alleviate the pain here within them tuning dungeons in a way that's unfriendly to beginners. There's nothing fun about spamming Art of War for the majority of a dungeon run.

For high end content: up healing not through artificial difficulty, but interesting healer-specific mechanics. Kefka Savage I think could be a good example, because even undersized healers have to work and do mechanics and not simply cheese it (well, not entirely, there are some cheese mechanics)

MP management: I feel like Shadowbringers has us nearing a point where MP is redundant as resource management. The only time I feel like I'm running low is if I'm having to res a lot. MP management I feel like is a feature of playing a mage class. Have people thinking about MP economy again, heck, people might start using piety materia more in progression runs if you do. This is what I did when AST had MP problems.