For most secrets they are under your control so, sure, go ahead and rotate them, allowing the old version to continue being used in parallel with the new version for 30 minutes or so.
For other secrets, rotation involves getting a new secret from some upstream provider and having some services (users of that secret) fail while the secret they have in cache expires.
For example, if your secret is a Stripe key; generating a new key should invalidate the old one (not too sure, I don't use Stripe), at which point the services with the cached secret will fail until the expiry.
If the attacker is moving with "surprising velocity," every hour of delay on an email blast is another hour the attacker has to use those potentially stolen secrets against downstream infrastructure. Using Twitter/X as a primary disclosure channel for a "sophisticated" breach is amateur hour. If legal is the bottleneck for a mass email during an active compromise, then your incident response plan is fundamentally broken.