Before Go 1.20, the RSA based TLS key exchanges used the math/big library, which is not constant time. RSA blinding was applied to prevent timing attacks, but analysis shows this may not have been fully effective. In particular it appears as if the removal of PKCS#1 padding may leak timing information, which in turn could be used to recover session key bits.
In Go 1.20, the crypto/tls library switched to a fully constant time RSA implementation, which we do not believe exhibits any timing side channels.