The RFC's dont technically deal with standards for code signing or TLS/SSL per se. Rather, they set the standards for x.509 certificates and PKI. Such as how you should construct a x.509 certificate using asn1 (RFC 5280) and then how it should be encoded to create a certificate.
The standards for TLS/SSL and code signing certificates which are issued by Certificate Authorities (CA's) such as GlobalSign, Digicert, Sectigo, etc are subject to the CA/B forum Baseline requirements. Code signing certificates for the Windows ecosystem fall into this category.
However, if you are signing code on Linux you might be using a PGP certificate and key to apply the signature. In this scenario, you would be using the PGP web of trust instead of CA's.
As I understand the SSL/TLS/https certificates rules are specified by the RFCs. Mixed use of servers and clients from different vendors will just interoperate without a problem. Does such kind of standard ways exist for software signing?
Code signing, document signing, TLS/SSL, S/MIME, are all examples of different types of x.509 certificates being used for different purposes. The x.509 certificate and key files are essentially cross platform because they all adhere to the same RFC's on how to construct and use the files. You can use the x.509 certificate to apply a digital signature to a file. How to construct digital signatures is (I think) in RFC 2315.
Or is that each software OS would use their own way of signing and need the package vendors to follow? Or ask in a specific situation, if the package signing is working well on a Linux system, would it work on other OS or platforms?
How each OS handles the signatures varies. Windows requires code to be signed using a code signing certificate issued via a CA. If the code is executing at the kernal level, then you have to buy a EV Code Signing certificate and submit the code to Microsoft for review. Linux however does not require code to be signed by a code signing certificate. Instead, Linux uses the PGP web of trust to verify PGP signatures in the repository. Packages ported from Linux to Windows will not be trusted on Windows because Windows doesnt use the PGP web of trust. Same in reverse, Windows applications ported to Linux will not be trusted unless you sign it with a PGP key and you import the PGP certificate into the clients PGP keystore. Apple also has its own requirements and you can find their documentation here.