As to the specs, note that 4.7 says

In RSA signing, the opaque vector contains the signature generated
using the RSASSA-PKCS1-v1_5 signature scheme defined in [PKCS1]. ...

referencing (then-current) RFC3447 which unambiguously defines the whole signature process: hash, then encode, then pad, then the RSA modular exponentiation.

Note that TLS DSA and ECDSA signatures are just the standard notSchnorr(hash(M)) but TLS1.2 (protocol) RSA signatures are PKCS1v1_5 which is in brief

$$\operatorname{modexp}(n,d) (\operatorname{add01FF...00} (\operatorname{DERSEQ} (\operatorname{hash}(M)))))$$

while in TLS1.1 and earlier they were a variant of PKCS 'type 1' or even 'type 0' $$\operatorname{modexp}(n,d) (\operatorname{maybe\_add01FF...00} (\operatorname{SHA1concatMD5}(M)))$$ -- as noted in that same paragraph. And TLS1.3 changes to PSS instead.

Meta: Mathjax somewhat better, thanks SEJPM.

As to the specs, note that 4.7 says

In RSA signing, the opaque vector contains the signature generated
using the RSASSA-PKCS1-v1_5 signature scheme defined in [PKCS1]. ...

referencing (then-current) RFC3447 which unambiguously defines the whole signature process: hash, then encode, then pad, then the RSA modular exponentiation.

Note that TLS DSA and ECDSA signatures are just the standard notSchnorr(hash(M)) but TLS1.2 (protocol) RSA signatures are PKCS1v1_5 which is in brief

$$\operatorname{modexp}(n,d) (\operatorname{add01FF...00} (\operatorname{DERSEQ} (\operatorname{hash}(M)))))$$

while in TLS1.1 and earlier they were a variant of PKCS 'type 1' or even 'type 0' $$\operatorname{modexp}(n,d) (\operatorname{maybe\_add01FF...00} (\operatorname{SHA1concatMD5}(M)))$$ -- as noted in that same paragraph. And TLS1.3 changes to PSS instead.

Meta: Mathjax somewhat better, thanks SEJPM.

As to the specs, note that 4.7 says

In RSA signing, the opaque vector contains the signature generated
using the RSASSA-PKCS1-v1_5 signature scheme defined in [PKCS1]. ...

referencing (then-current) RFC3447 which unambiguously defines the whole signature process: hash, then encode, then pad, then the RSA modular exponentiation.

Note that TLS DSA and ECDSA signatures are just the standard notSchnorr(hash(M)) but TLS1.2 (protocol) RSA signatures are PKCS1v1_5 which is

$$modexp(n,d) (add01FF...00 (DERSEQOIDandOCTSTRING (hash(M)))))$$ while in TLS1.1 and earlier they were a variant of PKCS 'type 1' or even 'type 0' $$modexp(n,d) (add01FF...00or1.0addnothing (SHA1concatMD5(M)))$$ -- as noted in that same paragraph. And TLS1.3 changes to PSS instead.

Meta: yes my Mathjax is ugly; anyone who knows how to improve it feel free.

As to the specs, note that 4.7 says

In RSA signing, the opaque vector contains the signature generated
using the RSASSA-PKCS1-v1_5 signature scheme defined in [PKCS1]. ...

referencing (then-current) RFC3447 which unambiguously defines the whole signature process: hash, then encode, then pad, then the RSA modular exponentiation.

Note that TLS DSA and ECDSA signatures are just the standard notSchnorr(hash(M)) but TLS1.2 (protocol) RSA signatures are PKCS1v1_5 which is in brief

$$\operatorname{modexp}(n,d) (\operatorname{add01FF...00} (\operatorname{DERSEQ} (\operatorname{hash}(M)))))$$

while in TLS1.1 and earlier they were a variant of PKCS 'type 1' or even 'type 0' $$\operatorname{modexp}(n,d) (\operatorname{maybe\_add01FF...00} (\operatorname{SHA1concatMD5}(M)))$$ -- as noted in that same paragraph. And TLS1.3 changes to PSS instead.

Meta: Mathjax somewhat better, thanks SEJPM.