I don't use IMAP because I don't want to leave my email on my email provider servers. I download messages over POP3, filter to folders (one per person or customer) and backup as any other file. I use K9 to read those messages over POP3 before I download them with Thunderbird. I delete notifications and anything that doesn't have to be stored forever. The obvious downside is that I can't access old mail when I'm away from my laptop (example: now.) Surprisingly this never turned out to be a problem for the last 30 years. Of course I didn't use K9 unless I had an Android phone in 2011.
However I see two ways to let my phone read old mail
1. Set up my own IMAP server at home and deliver email to it, then program some filter system to mimic what I'm doing in Thunderbird.
2. Access Thunderbird directory on my laptop over IMAP. That IMAP server would be on my laptop or (better) on some always on server at home that uses the same file format as Thunderbird. I would rsync it with my laptop.
I admit that number 2 is weird. Number 1 is the proper way but I have so little incentive to do it that I'll probably stick with my current setup forever.
Another option, hypothetical, is you export your emails to a common format like markdown (with embedded meta directly in each file; 1 per email or in a pair where the secondary file is the same name but stores meta only ie- in json) and then open them in any note-taking app or wiki or static site generator that works on markdown files (with some extent of configuration presumably, extra points if the app makes it sensible to easily organize your emails for optimal viewing). You could serve the files over HTTP, probably less hassle than running a secondary IMAP server, or alternatively you could sync them to your device(s) over ssh via git or zfs or an app like Syncthing.
Thunderbird to HTTP looks simple enough to be a side project sometimes in the future. It could integrate with a backup server I'm planning to setup. Thanks.
However I see two ways to let my phone read old mail
1. Set up my own IMAP server at home and deliver email to it, then program some filter system to mimic what I'm doing in Thunderbird.
2. Access Thunderbird directory on my laptop over IMAP. That IMAP server would be on my laptop or (better) on some always on server at home that uses the same file format as Thunderbird. I would rsync it with my laptop.
I admit that number 2 is weird. Number 1 is the proper way but I have so little incentive to do it that I'll probably stick with my current setup forever.