How does the 6502 execute the branching instructions? I looked at the schematic, but couldn't find anything.

Have you been following org's thread on the 6502 logic?
viewtopic.php?f=8&t=2208&start=39

On Balazs' giant schematic, there's some branch handling logic at the middle left, IIRC, but his orientation is upside down compared to visual6502, where you'll find it on middle right.

But you won't find a single section: there's quite a lot of work to do branches, so the relevant logic is spread around. The PC adjustment is done by the ALU.

Cheers
Ed