1. What do you think the basic fantasy of a Martial is exactly? For me and the people I play with, they're warriors who fight with weapons, and at high levels their physical abilities become super human, hence absorbing ambient magic as an explanation for that. We don't need them to be a nonsensichal pocket of low magic in an otherwise high magic setting.
2. As originally introduced in Naruto,
Sage chakra is 'nature chakra' one gathers from the world around them.
3. The occult spell list in Pathfinder2e is psychic stuff, lovecraftian horror stuff, Hags, Shadows, and etc. Bards cast with Occult in Pathfinder, so yeah, fits.