[new opmath] Deprecation warnings and making LinearCombination.compare more user friendly

[Qottmann]

Removing LinearCombination._obs_data, which requires updating LinearCombination.compare. While at it, also updating the doc string to make it clear.

Potential Drawbacks

A comparison with an Observable that has no pauli_rep (i.e. involving a Hadamard) will not work due to https://github.com/PennyLaneAI/pennylane/blob/master/pennylane/ops/functions/equal.py#L160. I consider this a separate issue for updating qml.equal accordingly. Alternative solution is to give Hadamard a pauli_rep.

op1, op2 = (qml.ops.LinearCombination([1.0], [qml.Hadamard(0)]), qml.Hadamard(0))
op1, op2 = (qml.ops.LinearCombination([1.0], [qml.Hadamard(0) @ qml.Hadamard(1)]), qml.Hadamard(0) @ qml.Hadamard(1))
op1, op2 = (qml.ops.LinearCombination([1.0], [qml.Hadamard(0) @ X(1)]), qml.Hadamard(0) @ X(1))

[sc-59339]

[github-actions]

Hello. You may have forgotten to update the changelog!
Please edit doc/releases/changelog-dev.md with:

• A one-to-two sentence description of the change. You may include a small working example for new features.
• A link back to this PR.
• Your name (or GitHub username) in the contributors section.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.68%. Comparing base (10d59e7) to head (2857505).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5504      +/-   ##
==========================================
- Coverage   99.69%   99.68%   -0.01%     
==========================================
  Files         410      410              
  Lines       38247    37944     -303     
==========================================
- Hits        38130    37826     -304     
- Misses        117      118       +1     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[trbromley]

Thanks @Qottmann!

[astralcai]

Looks good! Just a small comment.