I'm not sure why Bauer felt a need to analyze both 2...d5 (his repertoire recommendation) and 2...e5, because he doesn't give any explanation.
There is no bibliography, and the only external reference of any kind that I can see is a passing mention of Wisnewski (2007)
Play 1...Nc6! (see Bauer page 14). As for whether he has looked at chesspublishing material, it's hard to say. He does cover many (not all) of the same games that are in the chesspublishing archive, but his notes are different. My best guess is he used almost exclusively the ChessBase database and an engine.
Specifically to the lines you asked about.
1.e4 Nc6 2.d4 e5 3.dxe5 Nxe5 4.Nf3 - 4...Nxf3+ is his main line, following Korneev - Hoi, 2015 https://old.chesstempo.com/gamedb/game/3902811. He offers an improvement taking the game from +/- to +=.
- 4...Bb4+ "Trying to be creative with 4...Bb4+ can easily backfire. Some examples: ..."
- 4...Qf6 he gives 3 moves for white. One of them is 5.Nc3 and he mentions Plaskett - Sherwin, 2002 https://old.chesstempo.com/gamedb/game/2045437, which can be found in the chesspublishing archives.
- 4...d6 not mentioned.
1.e4 Nc6 2.d4 e5 3.d5 Nce7 4.Nf3 Ng6 (4...d6 Bauer says is a "valid alternative" with a paragraph of discussion but no actual variations)
5.h4 h5 6.Bg5 Nf6 - 7.Nc3 is his main line, following Christiansen - Benjamin, 2000 https://old.chesstempo.com/gamedb/game/2675186. Here is one of those places I would criticize him for not identifying critical tries for white. He gives a couple of one-move suggestions on move eight, but it's not really enough.
- 7.Nfd2 "This knight retreat was played in Chabanon, J - Canonne, A France 1991 https://old.chesstempo.com/gamedb/game/675551, and also makes sense. It resulted in a crushing White victory, but Black has many possible improvements."
If you think both 1.e4 Nc6 2.d4 e5 3.dxe5 Nxe5 4.Nf3 d6 and 1.e4 Nc6 2.d4 e5 3.d5 Nce7 4.Nf3 d6 are okay for black, then why not play
1.e4 e5 2.Nf3 d6 3.d4 Nc6!? ? Note that there is a chessable course advocating 1.e4 Nc6 2.d4 e5 3.Nf3 d6!?
https://www.chessable.com/the-aggressive-nimzowitsch-1-e4-nc6/course/104898/, which amounts to the same thing.
- 4.dxe5 Nxe5 is a transposition.
- 4.d5 Nce7 is a transposition.
- 4.Bb5, 4.Bc4, and 4.c3 are respectively Spanish, Italian, and Ponziani. These are bound to be += but are they really worse for black than 4.dxe5 or 4.d5?
I'm not
advocating this for black, just noting the possibility.