This is not strictly a self hosting answer, but given the problem you are describing, I think it is still relevant.

If you are already comfortable using an LLM based tool to manage email, take a look at SaneBox (this is not an LLM).

It is not an email provider and not an email client. It sits behind the scenes and works with almost any provider that supports IMAP, including custom domains. All the filtering, prioritization, and notification cleanup happens server side, so you keep your existing setup.

It excels specifically at what you are struggling with: automatically separating real human email from receipts, shipping notices, one time codes, and low value notifications, without forcing you into Inbox Zero workflows or Gmail specific features.