Caddy automatically staples OCSP for all relevant certificates. It will refresh the staple about halfway through its validity period. If the next status is Revoked, Caddy will replace the certificate right away.
(Can your other server do that?)
OCSP staples are usually valid for about 3-7 days. Caddy refreshes them about halfway, at which point it would notice the Revoked status and replace the cert. Give it 3-4 days at most.
Probably not safe to assume anything with regards to security protocols. That said, it'd be dumb (and harmful) for clients to disregard/reject completely valid, fresh, verifiable, signed OCSP responses.
May not be thinking this through correctly - but considering a firewall or something which independently does it’s own OCSP lookup and then blocks access based on that (especially a corporate ssl interception thing)