Remove Provider ABC (deprecated in 1.1)

[1ucian0]

Summary

Provider and ProviderV1 have been deprecated in #12145. This PR removes them.

[qiskit-bot]

One or more of the following people are relevant to this code:

• @Qiskit/terra-core

[coveralls]

Pull Request Test Coverage Report for Build 13573516292

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

• For more information on this, see Tracking coverage changes with pull request builds.
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• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 8 of 10 (80.0%) changed or added relevant lines in 1 file are covered.
• 40 unchanged lines in 4 files lost coverage.
• Overall coverage increased (+0.2%) to 88.103%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/providers/basic_provider/basic_provider.py	8	10	80.0%

Files with Coverage Reduction	New Missed Lines	%
crates/accelerate/src/unitary_synthesis.rs	1	94.39%
crates/qasm2/src/lex.rs	3	92.48%
crates/qasm2/src/parse.rs	18	96.68%
qiskit/visualization/circuit/_utils.py	18	94.44%

Totals
Change from base Build 13553732677:	0.2%
Covered Lines:	77504
Relevant Lines:	87970

---

💛 - Coveralls

[1ucian0]

Neko failure is blocked by the release of qiskit-community/qiskit-experiments#1490

[qiskit-bot]

One or more of the following people are relevant to this code:

• @Qiskit/terra-core

[ElePT]

The changes look good, but neko still shows that this removal breaks qiskit_experiments.

[mtreinish]

LGTM, 2 small tweaks in the release note. but I'll just apply those and approve.