
If you’re already using Debian on desktop, then Debian on a VPS makes sense from a maintenance perspective: you only have to track one set of security updates. When there’s suddenly a critical update for some vulnerability, you can update both at once because it’s the same upstream repos. Whereas with Ubuntu on your VPS, you’d have to be mindful to make sure to check back when the same vulnerability is patched there.
Do not underestimate the effort to upkeeping a server, and do try to unify your procedures so you’re spending less time doing the necessary things, and more time building up your self hosting stack.

Would cert-manager for Kubernetes be approximately what you’re looking for? In that particular case, it’s a service that runs in a K8s cluster, that can auto-request CSRs and send them to Lets Encrypt using one of the challenge types. It takes care of managing the returned certificates, such as renewing them before expiration and registering the private keys within the K8s key store.
I presume that you’re not already using K8s, so maybe that project will help you find the keywords to describe the sort of certificate manager that you want.