Deprecate qiskit.extensions

[kdk]

What is the expected enhancement?

Following #4699 and #4311 and others, the qiskit.extensions folder should be empty and can be deprecated and removed.

[mtreinish]

I opened up #10646 just now and missed that this already existed. I had these details in there about how we can go about making this change:

The qiskit.extensions module is a historical artifact that predates the existence of the circuit library. As we're stabilizing and unifying interface we should remove this standalone module and migrate or remove the classes defined in it. Right now there are the following things in the module:

• UnitaryGate
• Initialize
• Snapshot
• HamiltonianGate
• SingleQubitUnitary
• UCPauliRotGate
• UCRXGate
• UCRYGate
• UCRYGate
• Isometry
• DiagonalGate
• MCGupDiag
• UCGate

As a first step we should migrate these class definitions to live in the circuit library and add a redirect shim that will emit a deprecation warning for anything using qiskit.extensions. In parallel we should take inventory of these classes and individually deprecate any class which doesn't provide value anymore and stage those for removal.

[ewinston]

What are the thoughts about which of these should be deprecated?

[Cryoris]

@ewinston Only Snapshot and SingleQubitUnitary for now, I added some explanations in #10725.