I really like this progression, and I think it's useful of thinking about the whole thing as focusing around an F♯ tonal center. Major or minor? It's a little hard to say. The notes that are compatible with every single chord are F♯, B, E, so there's room for both major and minor. The resolution is to F♯Maj, but these progressions could very well have resolved to F♯min instead.
Here's my overall summary: the song is in F♯min, but with the i chord replaced with F♯Maj instead of F♯min. The first section draws on the family of chords in F♯ Dorian minor (with the i chord replaced by F♯Maj), and the second section draws on the family of chords in F♯ Aeolian minor (again with the i chord replaced by F♯Maj).
To start out, I think it's worth emphasizing that a song in F♯ Major can contain an A♮, and this makes sense on a theoretical level. Granted, this might seem to go against classical music theory, since A♮ is the flat third and any major scale should contain the major third. However, the F♯ Major Blues scale contains the notes F♯-A♮-A♯-C♯-D♯, where A♮ is a blues note. Your progression (and many other similar progressions) builds off this idea. The second chord of the song (AMaj) is built from that blues note (A♮), and that note (A♮) will work melodically over every chord in the song. This makes F♯min pentatonic (F♯-A-B-C♯-E) a great candidate for soloing/writing melodies. That one scale would sound good over the entire first progression, and it could give some nice continuity to the melodic phrases. (As an aside, it would also sound great to play F ♯Maj pentatonic - A Maj pentatonic - B Maj pentatonic, but this isn't the cohesive description you're seeking. Or you could even play F♯ Maj pentatonic over m. 2-3 and F♯ Maj pentatonic over m. 1 & 4.)
So, I would describe the first section as I-♭III-IV-I, with the note that I-♭III doesn't really disrupt the presence of a single tonal center.
As for the second section, I think it mostly fits in this same idea of F♯Maj/min. Just as F♯Maj-AMaj-BMaj-F♯Maj sounds great, so would DMaj-EMaj-F♯Maj. (This ♭VI-♭VII-I progression is part of the Mario Bros. theme song.) However, two chords (CMaj-GMaj) are an exception. These chords don't support an F♯ min pentatonic melody, and they don't really fit into a description of the song as being in F♯ Maj. Accordingly, their function can be explained as a parallel movement. Essentially, you're repeating the DMaj-AMaj (♭VI-♭III) progression, just down a whole step. That sort of technique sounds great when well-placed, as it is here, and it's a good tool to have in one's bag of composing tricks. So I'd describe the second section as: [♭VI-♭III in F♯]-[♭VI-♭III in E]-[♭VI-♭III in F♯]-IV.
Overall, here's how I'd suggest thinking about this:
- 1st section is I-♭III-IV-I in F♯
- 2nd section is ♭VI-♭III-[♭VI-♭III in E]-♭VI-♭III-IV in F♯
If you want to go deeper into other chordal options, you can think of it like this:
- 1st section is in F♯ Dorian minor, but with the i chord replaced with F♯Maj
- 2nd section is in F♯ Aeolian minor, but with the i chord replaced with F♯Maj
Accordingly, other chordal options available to you might include any progression in F♯ Dorian minor or F♯ Aeolian minor, but with the i chord replaced with F♯Maj. For example: