There is limit of 5 duplicate certificates per week (where “week” is a sliding window of 7 days; limit doesn’t get reset on specific day of week). Regarding revocation, here’s relevant part of rate limits description:
Revoking certificates does not reset rate limits, because the resources involved in issuing the certificates have already been used.
You could simply copy all Let’s Encrypt files from the old server and they would work - but as you’ve already revoked your certificate (I would recommend revoking certificates only if private key gets compromised), now you have to wait…
… or you have to use “loophole” in rate limits. Certificate is counted as a duplicate, if it has exact same set of hostnames. Hence, if you request a new certificate for heidelberg.yaroscloud.com and (for example) www.heidelberg.yaroscloud.com, it won’t be treated as duplicate one.
Please note that there is also a weekly limit of 20 certificates per domain.
Staging server is used only for testing purposes; certificates it issues are not publicly trusted (“not valid”, as you said).