I am wondering why TheoryTab, Hookpad, etc. prefer F♯-Major instead of G♭-Major. G-flat major has six flats and F-sharp major has seven sharps. Wouldn’t it make more sense to use the one with less accidentals?
As Quentin already pointed out, F# and Gb have the same amount of accidentals. I would say the advantage of F# over Gb is that you’re unlikely to introduce more accidentals when borrowing chords from parallel modes, as Lydian is the only diatonic mode brighter than Ionian. On the other hand you’re still going to end up with double sharps when introducing secondary dominants, so I guess there’s no real winner here.
What the hell is going on with that Cheat Sheet though? Every damn example on that page is in F major. People with perfect pitch are going to go crazy when hearing those examples