Its implementation requirements (§3.1) are telling: HS256 is the only JWS algorithm marked Required, RS256 is Recommended and ES256 is Recommended+ (expected to become Required); PS256, the other ES and RS variants and none are Optional. Notable rules: HMAC keys must be at least as long as the hash output (§3.2); ECDSA signatures are raw r‖s (§3.4); RSA keys must be at least 2048 bits (§3.3); ES512 uses P-521.
For JWE it defines key management (RSA1_5, RSA-OAEP, RSA-OAEP-256, A128KW–A256KW, dir, ECDH-ES and ECDH-ES+AxxxKW, AxxxGCMKW, PBES2-HS256+A128KW and friends) and content encryption (A128CBC-HS256, A192CBC-HS384, A256CBC-HS512, A128GCM, A192GCM, A256GCM). The IANA registry is where new algorithms land, including ES256K (RFC 8812), Ed25519 and Ed448 (RFC 9864) and, in drafts, ML-DSA.