I’d say that Italy needs some German help in the Med, but the question is, how much exactly. Three carriers and an air base seems like a lot of German money not spent on fighting Russia. Any planes based on those carries would also find it difficult to make as much impact on the Eastern front as they would normally do.
Germany may send a few of its planes to Southern Italy to scramble against the UK attacking the Italian fleet, or to sink the French fleet if Italy can’t do that.
Bulgaria - I’d normally prefer to have it as Germany and use that infantry against Russia. Yugoslavia is another matter, because Germany can strafe it from Southern Germany on G1, plus one inf from Rumania, and retreat all units to Romania after one round of fighting. That’s a pretty common maneuver to get those units to the Russian front quickly. Italy can then take the weakened Yugoslavia. As for Greece, I prefer to take it with Italy because it’s unattractive to divert German units there.
Gibraltar is important of course - try to hold it for as long as possible to keep the US out of the Mediterranean.