Does muting re-encode the video?

No — the audio track is simply dropped and every video byte is copied through. It's instant even on large files, with zero quality change.

Can I get the audio back?

Not from the muted copy — keep your original, or use Video to MP3 first if you want to save the soundtrack.

No — the video never leaves your device. Muting happens locally, which is also why it finishes as fast as your disk can copy the file.