ECDSA signature with Brainpool curves in TLS possible? Even the up to date RFC 8446 lists at the page 41 as the options for the ECDSA in e.g. TLS_ECDHE_ECDSA_WITH_... only NIST curves:
      /* ECDSA algorithms */
      ecdsa_secp256r1_sha256(0x0403),
      ecdsa_secp384r1_sha384(0x0503),
      ecdsa_secp521r1_sha512(0x0603),

Does it mean that the certificates containing the public key based on Brainpool curves cannot be used for
signing the (EC)DHE parameters in SERVER KEY EXCHANGE?
RFC 8734 defines how to use Brainpool curves within TLS 1.3, including how they can be used in ECDSA signatures (section 4)
.  Hence, yes, there is an official way to negotiate Brainpool curves for use in the SERVER KEY EXCHANGE.