Those would be my top 3 personally.
Power usage would be an interesting problem as well, because I'm not sure if keeping a socket open would pin the radio active.
I haven't seen any suggestion the radio is being pinned active - it seems to still sleep fine, and I believe an incoming messages triggers a downlink page to the phone, which will then wake the radio to deliver the packets.
However, I wasn't able to make FairMail to deliver without a considerable delay either—despite it displaying a notification and being excluded from ‘battery optimization’. But apparently it's just me.
On "pure" Android (thinking Pixel, and the relatively pure Motorola devices, etc.) there's no delays at all - it's really impressive. I'll get the notification on my phone consistently before on my PC.
These limits don't apply to notifications via Google's services (GCM or whatever they're currently called). So if you're using the Gmail app or another app for a specific mail service, sure you will receive push notifications quickly.
As you say, Google is making it a lot harder, but FE with a foreground notification seems to do this fine for me.
It's easy to change an app's background ability in Android. By default apps are forced into the background, but if you change that your k9 email will notify you all day long (it does support IDLE)
The issue is even older than I thought, though I was pretty sure the requirement for a notification specifically appeared around Android 8 or 9.
Also, seeing as K9 doesn't look to be anywhere near frequently updated, I'm not expecting this to change soon.
P.s also f-droid here (ps you can donate with crypto if you want)
Am now a happy user of Fastmail with BYOD(omain). =D