TLS 1.2 Server Key Exchange problem
You're wrong. This is a difference between TLS 1.2 and 1.3.
In 1.2 SignatureAndHashAlgorithm identifies only the algorithm (not curve) and hash. In 1.3 SignatureScheme does identify the curve for ECDSA, and the certificate OID for RSA-PSS. See the next to last para on page 44:

[1.3] ECDSA signature schemes align with TLS 1.2's ECDSA hash/signature
pairs.  However, the old semantics did not constrain the signing
curve.  If TLS 1.2 is negotiated, implementations MUST be prepared
to accept a signature that uses any curve that they advertised in
the &quot;supported_groups&quot; extension.

(although in 1.2 and lower before RFC7919, that extension was elliptic_curves not supported_groups!)
Wireshark is showing both decodes: the single, combined SignatureScheme name for 1.3, and the separate hash+signature names for 1.2, and only the latter apply in your case. This is arguably a bug: some other places this field occurs it could be ambiguous whether to use the 1.2 or 1.3 interpretation, but ServerKX can (occur and) contain this field only in 1.2 so it should have the 1.2 interpretation.
And the brainpool curves are designed so that standard (X9.62) ECDSA works with them. Edwards curves as such cannot, but (IINM) they can be converted to Weierstrass curves which can.