Just at a glance...... I like White here. Better development, blacks pieces are passive. White has the bishop pair as well as open g-file bearing down on blacks king which is already under the hot seat.
For white I see 2 plans. 1 is to develop the knight, double rooks and try to increase pressure, however that may give black time to get some pieces out make white's exposed king uncomfortable.
Second plan, which I like, is f6 immediately.
This defence is rarely used by the Black players, but IMO as White I found it very unpleasant to play against this (actually I wasn't prepared at all for this, and finding good moves for White OTB with only limited time available is very hard):
I'm wondering who is better in the final position of this variation. White is up a pawn (for the moment), but their ugly pawn structure looks like in the long run they will actually be down a pawn, and also White's uncastled king seems to be a disadvantage for White. Anyways, White's forces are not well coordinated, especially their Rook g2 seems to be in a suspicious position. The only plus for White may be their bishop pair, but Black's structure seems to be solid enough that White's bishops won't find targets for attack easily.
I'm wondering where White could've played better to avoid this desastrous endgame, because IMO Black is better here.
So what is the correct way for White to deal with this 'improved' version of the Schliemann's Gambit?