Any chance your web server is configured with both an ECDSA and a RSA cert, and the RSA one happens to be the self-signed certificate you’re seeing there? Maybe some leftovers somewhere in your config.
Web servers that implement this hybrid setup typically select the certificate based on the cipher suites the client offers. If openssl s_client doesn’t offer any ECDSA suites (not sure if this is the case), the web server will use the RSA certificate. Firefox offers ECDSA suites, so that’s probably why you’re getting the correct certificate there.
Anyhow, independent of what the underlying issue is, that certificate does not look remotely like anything Let’s Encrypt would issue, so you’re probably better off focusing your search on areas that are not specific to Let’s Encrypt.