[BWC and API enforcement] Introduce checks for enforcing the API backward compatibility

[reta]

Is your feature request related to a problem? Please describe.
This is the final goal, once we have the API outlined (annotated with @publicapi), we could enforce the compatibility rules that have to be applied between version.

Describe the solution you'd like
The japicmp, that was explored here #9044, is one of the most advanced tools we could use for these purposes.

Describe alternatives you've considered
A clear and concise description of any alternative solutions or features you've considered.

Additional context
Part of #8127

[peternied]

@reta I think we've got enough surface area to start enforcing the Public APIs. When building up #9303 we could add checks alongside it, what do you think?