Deprecate PauliTable and StabilizerTable

[ikkoham]

Summary

Continue #7245 and #7269

Details and comments

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[coveralls]

Pull Request Test Coverage Report for Build 4675731275

• 13 of 13 (100.0%) changed or added relevant lines in 3 files are covered.
• 2 unchanged lines in 1 file lost coverage.
• Overall coverage decreased (-0.02%) to 85.418%

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Files with Coverage Reduction	New Missed Lines	%
qiskit/extensions/quantum_initializer/squ.py	2	80.0%

Totals
Change from base Build 4672911381:	-0.02%
Covered Lines:	67700
Relevant Lines:	79257

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💛 - Coveralls

[Cryoris]

Some small comments otherwise LGTM 🙂

[Eric-Arellano]

Hi, please use the new @deprecate_func decorator that landed today instead of @deprecate_function. See #9864 for an example.

It should make things easier for you because it auto-generates most the message :) The only part that needs to be manually worded is additional_msg, where you'll usually want to say something like "Instead, use ``blah blah``."

[Eric-Arellano]

Deprecators look good. Thanks!

[jakelishman]

Thanks Ikko, after the slog that was #7269, I think we're finally in a position where we can do this safely (in as much as deprecations/removals are ever safe). Thanks for sticking with it.

I'm very encouraged that there's no real modifications to any code other than the deprecated components, including in tests; it's a good vote of confidence that we're not relying on these deprecated classes internally.