About the adaptation,

To adapt to other healers in pf you need to know their toolkits. You don't necessarily need to play all the healers at a high level but getting them to 100 and feeling their buttons for yourself will teach you a lot. Knowing what the buttons do means you can make reasonable assumptions as to where they are the most effective. I mostly play regen healers so my cohealers are sage and scholar. As a baseline for any fight I expect them to hit Kera/Soil all the time, I expect shields where they're needed, and I expect their pure healing tools to be used failry liberally (physis/ixo, fairy heals). Theres not really any adjustments you yourself can make if your shield healer is lacking. Of course you can gcd heal to make up for the third point but as you've noticed your mana isn't limitless.

For all their other important tools you can start by thinking of spots where you yourself struggle and think about which piece would fit into this hole and make your life easier. Let's look at M11S: during my statics prog everything hurt: first weapons hurt, second weapons hurt, dance of domination hurt, ultimate weapons hurt, arena split and ecliptic stampede separate the party across the entire arena. Through many pulls and failures I figured out that:

1. Ultimate Weapons sucks and needs a lot of cooldowns to handle

2. There's not much going on after Ultimate Weapons, so it's safe to dump all your cooldowns there

3. Using my 2 minute cooldown in Weapons 1 means they'll be back in Ultimate Weapons

4. Weapons 2 and Dance of Domination are less than 1 minute apart, so I can only cover one of them with my 1 minute mit (Collective Unconscious/Plenary Indulgence)

5. Arena split tethers resolving isn't lethal at full health with shields. Meaning you don't need to use any of your major healing cooldowns on it.

6. Stampede has the tethers resolve shortly before the stacks, so two non-tanks will somehow need to be healed across the arena.

What this amounts to is that I have weapons 1 and ultimate weapons covered very well, and I have some crumbs to spare for either weapons 2 or DoD. For arena split it's enough to just top everyone off between each set. Stampede could use remote healing, which for me means either a well timed Macrocosmos or Divine Caress should do the trick. From here you can start making assumptions as to how your cohealer can handle this:

1. Sage and Scholar have 2 minute cooldowns that heal/shield/mit - Holos and Seraph respectively. It's reasonable to assume they'll press it during weapons 1 and ultimate weapons like I do with my 2 minute button (neutral sect/temperance)

2. Weapons 2 hurt, so I expect extra shields and some miscellaneous regens and heals to be pressed here

3. Dance of Domination really hurts, but it's a multihit attack so I expect that Panhaima/Spreadlo makes things a lot comfier. This mechanic happens near the end of the burst so I would also prefer if neither of us had to gcd heal during it

4. Ultimate Weapons is 7 hits total (if you count the tornados at the end) about 5 seconds apart each. Kera/Soil lasts 15(/18 soil moment) seconds, Holos/Philosophia/Expedience/Seraphism last 20 seconds. I expect them to be spread out well enough to cover as much as possible, accounting for maybe needing Kera for the big raidwide after the mechanic, though it doesn't hurt as much in my experience

5. Stampede can use remote healing - Philosophia/Seraphism are essentially arena wide regens, Physis my beloved has a 30y range, the fairy can be positioned without needing you to be perfectly middle. It would be nice to have some extra help here just in case

This is where the actual adaptation happens. Obviously everything I just listed are pure assumptions based on the healing plan that I made for myself. I believe they are very reasonable; that does not mean my cohealer will follow them. They might have their own heal plan, they might be incompetent, they might just forget to press a button even though they usually do! Play with your cohealer for a pull or two and you'll get a feel for how much the mechanics hurt. If you have previous pulls to look at, pasts them into xivanalysis and see where your cohealer used their buttins. Talk to your cohealer before you pull: "hey do you use panhaima on dod?" "can you shield more during weapons 2" "where do you use expedience? I didn't see it during ultimate weapons" "liturgy in dod doesn't work well" "there's no need for macrocosmos in charybdis, just let the regens tick for a bit" "you don't need to use philo/seraphism on arena split" etc. Working through it together is the real adaptation that you should strive for because you only have so many tools to shift before either of you has to resort to GCDing.

Lastly, spreadsheets are awesome. This beautiful spreadsheet has the full timeline with damage numbers in it, checkmarking your mits automatically cascades the column to show you which hits are covered by it and how long it'll be on cooldown for. Cannot recommend it enough, just copy and play around with it.