I need something like “smart notifications” to only notify for important emails, and not all my incoming emails
Group emails (like what Gmail do), for exemple Newsletters, Notifications/ Promotional, …
To make this work with Mail.app, you can use server-side filter rules to sort stuff into respective folders. The big advantage of course being that it doesn't depend on what your client can do (but if you can't use server-side, you can also set up rules directly in Mail.app itself). As for notifications, you can filter them with a "Smart Mailbox" (including checking that it's in a certain folder so you can re-use the rule processing) + setting message notifications to only trigger for that smart mailbox.