Precisely. The toolkit appears to be a rebranding of the ISARA Radiate™ Quantum-safe Toolkit. This is a patch for OpenSSL to include support for various Post-Quantum candidates.
You can use this tool to generate various (self-signed/untrusted) PQC certificates and then do key exchanges/establishments with them. None of this is bound to any certificate authority.
I am not aware of any. Please note that every publicy trusted certificate authority (such as Let's Encrypt) is bound to the CA/B baseline requirements, which currently does not allow issuance of any post-quantum key type. Any testing officially supported by Let's Encrypt would have to be done using untrusted environments (e.g. Let's Encrypt staging).
A major issue is that there is no full consensus yet about post-quantum algorithms. NIST intends to standardize at least three digitial signature algorithms - which could be used for certificates, plus new key encapsulation methods. There is no definite plan as to where to go, what algorithms should we use, what parameters, how should we mix them with classical crypto? There are lots of ways to mix different algorithms in a PQ certificate chain and it isn't yet (entirely) clear which one is best. PKI as a whole could change drastically.
Thus it feels a bit funny to do "testing" when we've no idea how the PQ certificates are going to look like. The DigiCert guide instructs to generate an eXtended Merkle Signature Scheme root (not a traditional signature scheme), a Dilithium intermediate (NIST intent for standardization) and a Rainbow leaf certificate (NIST PQC round 3 finalist; will not be standardized due to security concerns).
I would love to have a Let's Encrypt staging environment for PQ, but please let's sort out the algorithms before we get ahead of ourselves 
. Any local testing - for example, to test out the above algorithms - can already be done using early-adopter crypto libraries.