scandinavian opening: 3. .... Qe6 4..... Qg6

The 4 .... Qg6 is the theme. The chapter chess.com/ opening contains only very very basic information.
Is the move 4 .... Qg6 trendy as a modern variation or is it outdated, considered as a bad move?
What should White play in move 3 and 4?
Has anyone experience to share?

Qe6 is not a good move. Qa5, Qd6, and Qd8 are all fine. Qa5 is more traditional and allows more attacking chances but the modern Qd6 is solid. The Scandinavian is a fine opening but it violates opening principles to an extent. Qe6 is too much.

I share all those opinions because I think the Queen g6 position leads to thinking that the pawn g2 would be attacked. Nevertheless White can continue in the spirit of a gambit, offering the g2 pawn for fast development with 2 ideas:
1 castling Queen side and using the already open g-file for attack’s on Black having castled King Side. Giving a pawn for that advantage is not too expensive.
2 chasing the black Queen and get development advantage, then castling Queen side and using the
development advantage to attack Black having castled Quee Side. In fact, Black cannot castle King Side after Qxg2 Tg1 except if he likes dangerous situations for himself.

forget Q scandinavianm!

play the Nf3 marshall!

or don't. i quit Qxd5 in the 90s. i'm a tactician.

Books don’t indicate Qg6.
It’s computer that suggests Qg6.

It reminds me the g5 move.
It can be good but considering the risk and complexity it’s common not to play that.

By g5 move I mean pawn g2-g4-g5 in a pawn storm on a castled king in an opening different to Scandinavian.

none of the above! you aren't getting ANYWHERE near your book with me...

1.e4 d5 2.d4!? the blackmar diemer gambit... wayyyyyyyyy sounder than the tennison gambit. i used to play that. it performs poorly and the book sucks! no theory and literally falling apart at the binder on day 1.