Interesting about the mega database. I still think given it has been played 67 times by players 2500 or higher according to chess.com and it has a positive win rate over a larger sample size of games recorded on this database, it is a reasonable opening choice. Not the best but certainly an option to "shake things up" like you said. Of course a small percentage of these games are below master level, but from a practical point of view these games are relevant too. Unless perhaps you are a master only playing other masters.
Against 2. Qe2 2. c5 is surely the move. I am seeing in most lines white just transposes to a KIA setup. I found the following line interesting though, and I'm not really sure of the best way to play it. The top played move is 4. g6 which seems strange.
I 100% agree that 2. d4 is the best move. I am spending time looking at these other lines though in case I encounter them. If some of the world's best players get tricky with these "off beat" lines, there's no reason to think I will not be challenged with them at some point too.
2. Nc3 and Nf3 don't seem to do much because black just goes 2. d5. It seems hard for white to not just play d4 anyways.
2. c3 is a new one for me. I don't even think I have ever played against it. Will have to look into it. Not really sure what the point is. I guess I would just play 2. d5 and see what white does.
Can 2. b3 really be considered dubious though? It has a positive win rate and lots of GMs have played it. It is just another somewhat reasonable alternative to 2. d4. Dubov played it just recently at GM level in 2021. It's not like you're just playing h4 or something just to get an unexpected position.
Is it losing on the spot? No. But it definitely gives away your opening advantage and places White in a questionable position (especially when you fianchetto queenside and castle long).
In the Mega Database, up to 2020, there were 230 games played at the master level (almost all of them Blitz or Rapid), with White going +65=92-73 (28.3%/40.0%/31.7%, respectively). So yes, I would put it in the "dubious" category. You are going to see guys like Rapport, Duda, Van Foreest, Dreev, etc play things like that because they like to shake things up.
2. Qe2 seems like it is trying to transpose into a KIA without tipping your hand too early in hopes that Black either doesn't know how to play against the KIA or walks into a move-order issue. The main problem seems to be what do you do when Black responds with 2...c5? You've just transposed into an e6-Sicilian where Qe2 looks rather silly (as you would much rather have played Nf3).
I just don't understand, why look for weird sidelines when the simple 2. d4 is principled and strong (and objectively, the best move)? If you really want to deviate on move 2, why not just play Nc3 or Nf3? At least those moves will be useful in most lines. Or maybe even c3?