Does XChaCha20 exist with similar properties to XSalsa20?
Unfortunately, there is no specification for XChaCha20. But several implementations provide a HChaCha20 function, built the same way as HSalsa20.

XChaCha20 can be built with HChaCha20 + ChaCha20, and the security proof is similar to the one for XSalsa20.

The Libsodium documentation has a section on HChaCha20, which includes a code snippet to build XChaCha20 out of it.