fetchmail to an IMAP proxy with filtering?

I've needed to improve my email situation for a while. Right now, I have 
my personal mail hosted on Office 365. I just IMAP it off into 
Thunderbird on my desktop, laptop, and phone. Two major problems with 
that setup right now: first, I keep getting rate-limited on IMAP from 
Office 365. Secondly, the filtering provided by the service is very 
limited and doesn't always work great.

So I was thinking, it's got to be possible for me to setup a kind of 
client-proxy, right?

I'm thinking:
- Fetch 100% of the messages/content/etc from upstream IMAP to my server
- Use [local filtering mechanism of some kind] to filter them into
   trash or specific folders. I'll note: spam filtering is handled pretty
   well by Office365, so that's outta scope. This is more about putting
   mailing lists in their proper folders reliably, and regaining some
   power over things like github and gerrit e-mail notifications.
- Host an IMAP server that I can then point at this filtered, downloaded
   message content and feed it all to as many devices as I want without
   fear of rate limiting.

A couple of extra requirements I have:
- Any sorting done locally (e.g. filtering mailing list posts to a
   folder) needs to *also* happen on the upstream origin IMAP server. I
   want it to remain the source of truth and for webmail to still be
   useful.
- Ideally I can handle multiple accounts *with multiple logins*
   transparently. Imagine right now I have a Thunderbird account pointed
   to [email protected] at outlook.office365.com -- I want to just be
   able to change that to personal_email_tld (or similar -- not a shared
   login account) and have it transition over smoothly. If that's not
   possible, I still want a solution where 1 login = 1 email account,
   and not one where top-level folders map to specific accounts.

I'm asking on the list because... well, first of all I've never done 
this, but also, I just have no idea of the 2026 state of the art of 
these tools. I'm hoping someone can help. I've worked with email a lot 
generally, but all on the server/hosting side and all 15+ years ago so I 
know the protocols just maybe not the best tool choices.

Any help you can provide is appreciated!

Thanks,
JayF

P.S. I know there will be folks saying "change hosting". I'm not going 
to do that; as that would be disruptive to other family members on my 
domain. Either way, if I solve this myself the hosting becomes less of a 
concern generally.