Remove Provider as a parent class

[jyu00]

What is the expected feature or enhancement?

Qiskit is deprecating the Provider interface (see Qiskit/qiskit#12145). QiskitRuntimeService still inherits from Provider, and it wouldn't be a very good experience if everyone starts getting a deprecation warning every time they use Qiskit Runtime until the release of 2.0, especially since there is nothing they can do about it.

Provider today only has 3 methods:

• get_backend() - we can deprecate this in favor of backend()
• backends() - we already overwrite this
• __eq__() - we should define this method with a proper comparison (e.g. including channel, credential, instance, and channel_strategy)

Acceptance criteria

• Stop inheriting from Provider
• Update the Provider related methods as described above
• Update docstrings as needed, related to Replace get_backend with backend in the README #1261
• If possible, issue a deprecation warning if isinstance(QiskitRuntimeService, Provider) is used.

cc @1ucian0