I'm pretty invested in the Notion ecosystem, using Notion and Notion Calendar, and they've just rolled out Notion Mail which is absolutely superb. The killer feature is AI filters, letting you define your filters with natural language, and the model figures out where to put it and learns from future manual categorisation.
You can then optionally configure it to split the matching messages off from the inbox - they stay in the inbox as far as Gmail is concerned with a label applied, but are optionally moved to a separate section in Notion Mail.
It doesn't yet have the feature I would have thought would be obvious, which is passing an email into Notion proper, but I can't imagine it's not on the roadmap. I've prodded them about it, anyway.
Requires Gmail or Google Suite, but I think most of us use that. Don't think it requires you to use Notion.