QUIC does use TLS, but since TLS sits on top of TCP and QUIC replaces TCP entirely they wire TLS directly into their protocol rather than it resting on top as it does with TCP.

Technically this was fairly complicated to do, but cryptographically nothing much really changes, except that now more things are encrypted.

Now, if your TLS implementation just presents as a shim layer between a TCP port and your socket code then this may mean a significant rewrite, but again that's not about cryptography it's just an engineering problem.