I counted by hand, so it might be wrong, but they appear to list and link to 86 different ACME client implementations across more than a dozen languages: https://letsencrypt.org/docs/client-options/
I've used their stuff since it came out and never used certbot, FWIW. If I were to set something up today, I'd probably use https://github.com/dehydrated-io/dehydrated.
Plus, it's one of the easier protocols to implement. I implemented it myself, and it didn't take long.
So you're absolutely not dependent on the client software, or indeed anyone else's client software.