GnuTLS 3.6.x has been marked stable with release 3.6.5. Binary packages are available in experimental. - Please test! FWIW I have rebuilt all reverse build-dependencies without finding GnuTLS-triggered build errors.
GnuTLS 3.6.x is ABI compatible with earlier versions. However the addition of TLS 1.3 support might require source changes. Due to differences in the TLS 1.3 handshake GNUTLS_E_AGAIN can be returned for blocking sockets.