Posts that are either liked, marked as solution, or replied to by a Core Member should automatically skip review

I agree, this'd be nice to have. (Actually I started working on this a little bit a while ago but then other things came up in-between)

Seems this will be fixed in the next or next-next version — working with this now.

( There's also a bug (or unimplemented feature) if an admin / staff user attempts to edit a not-yet-approved post:
unimplemented("Updating visible post counts when post approved via an edit", "DwE5WE28") )

by a Core Member

Hmm maybe for simplicity, initially this'll be for edits and replies posted by staff only.
(I'd think admins would want to configure if interactions by Trusted Members, or Core Members, or only staff, should resolve review tasks.)

This now implemented, and deployed to Prod (yesterday). So hereafter there should be a bit fewer moderation tasks for you.

1) Posts that get shown directly, but got added to the moderation queue for staff to have a look at, later: (the Review after published settings)

If a Core Member or staff replies to, likes, accept an answer, edits, changes to wiki — then that post is considered reviewed.
(I wrote staff before, but I think what you initially suggested in the title — core members & staff — is a better default).

2) The Require approval before settings, i.e. posts that are hidden until staff has approved them:
These won't get implicitly approved by any of the actions above.
Instead, there are new Approve and Reject buttons, on the discussion pages, just below the posts, which mods & admins can click to explicitly approve the posts without jumping to the moderation page.

Would be interesting to hear how this works for you