validate: make the Claude review opt-in

validate was the last workflow still spending a Claude review by default:
its reviewer set was derived from `skip` alone, so an unconfigured run
scheduled both providers. Every other caller already reached the verifier
through code-verify, which defaults to Codex.

Take the router's own vocabulary — reviewProvider codex|claude|both,
defaulting to codex — and forward it through full-check so /pre-pr can
still ask for the second reviewer.

Skipping a reviewer that was explicitly selected is contradictory input
and now throws: otherwise `reviewProvider: 'claude'` plus skip:['review']
would report green having reviewed nothing. Skipping the default reviewer
stays legal but is logged, since skip:['codex'] used to mean "review with
Claude" and now means no review at all.