[throwaway81523]

I use K9 because Fastmail's client is closed source and not on f-droid (I don't have a google play account). It works ok for me as a secondary/occasional email client (main one is on laptop). It does miss notifications. I have heard somewhere that the only way to get reliable notifications involved using a google play service, which I didn't want to allow. I usually have mobile data on my phone disabled anyway, unless I am actually about to use it. But, I think other people use their phones a lot more than I do. I'm in front of a real computer almost all the time, so the phone is just in case I have to check something while away.

[ptidhomme]

I think you can set it up to get pull notifications (like every 15 or 30 min), and then disable "battery optimisation" for the app (that is, set it to "no restriction"). In my experience (my wife's GrapheneOS phone) it doesn't drain that much battery anyway.