Revert "Revert memory-owning expr.Var nodes (#11667)"

[jakelishman]

This reverts commit 052d889.

This gets us re-started on #10922.

[qiskit-bot]

One or more of the the following people are requested to review this:

• @Qiskit/terra-core

[coveralls]

Pull Request Test Coverage Report for Build 7931811688

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.
• To avoid this issue with future PRs, see these Recommended CI Configurations.
• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• -10 of 259 (96.14%) changed or added relevant lines in 8 files are covered.
• 15 unchanged lines in 2 files lost coverage.
• Overall coverage increased (+0.02%) to 89.283%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/circuit/classical/expr/expr.py	16	17	94.12%
qiskit/circuit/store.py	33	35	94.29%
qiskit/circuit/controlflow/builder.py	45	48	93.75%
qiskit/circuit/quantumcircuit.py	132	136	97.06%

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	3	91.69%
crates/qasm2/src/parse.rs	12	95.77%

Totals
Change from base Build 7923082089:	0.02%
Covered Lines:	59125
Relevant Lines:	66222

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💛 - Coveralls

[mtreinish]

This is a straight revert, lets restore this on main now so we can finish the feature for 1.1.0.