All issued certificates can be downloaded from Certificate Transparency logs aggregators like https://crt.sh/. But that won't help you if you don't have the private key any longer.
Seriously though, you will often see two entries for just one cert as there is a Precert and the final Leaf. I see 5 unique issued certs today which is the limit Let's Encrypt allows per week for "identical" certs. See Rate Limits for details
This may be the problem you have about not being able to issue another one. LE returns a specific error message in this case but Synology often translates that into one of its own. Synology itself sometimes gets "stuck" or blocks repeated requests and gives the same error message which makes this hard to debug.
The Synology forum is probably the better place to get assistance. It will come down to getting it back to a stable state and possibly waiting a week until you are past the LE rate limit block. There is a work-around at the Rate Limit page but I am not sure how viable that is for Synology DSM
