Love it. One of the major challenges with email is that a lot of disparate content is mixed together.
I run a product called Inbox Zero (if you google the term we're the ones that come up first). I often suggest to users that they aim for "Reply Zero". They might get 100 emails per day, but only 5 need a reply. As long as those are handled they're probably good.
One of the challenges people face is that there's so much noise mixed together. Newsletter, conversations, receipts,... what you call "DBTC", and it's time consuming to sort it into buckets. And frankly, before AI it might not have been worth the effort. But with AI assistance, it's actually very doable. Inbox Zero offers it, as do a bunch of others. What you call DBTC could potentially be sorted for you into that folder automatically.
PS. not trying to shill our own product. It's open source so you can even self-host it without paying us anything.
Free to self-host.