Adapting generators to opmath enabled/disabled

[PietropaoloFrisoni]

Context: After enabling the new operator arithmetic by default, we want the generators in the source code to return a LinearCombination instance or a Hamiltonian instance wherever possible.

Description of the Change: The generators touched in this PR are modified so that they return qml.Hamiltonian instead of Sum, Prod, or Sprod instances. When opmath is enabled, qml.Hamiltonian points to pennylane.ops.op_math.linear_combination.LinearCombination, and when it is disabled, it points to pennylane.ops.qubit.hamiltonian.Hamiltonian. This ensures that the appropriate instance is used consistently.
Note that the generators unchanged in this PR are modified (wherever possible) in #5410 , #5411 , #5412 (including the changelog entry).

Benefits: A more coherent choice depending on whether opmath is enabled or disabled.

Possible Drawbacks: None that I can think of, except that old opmath would be deprecated in the future. Therefore, some precautions that have been taken here (to ensure that tests associated with generators work even with opmath disabled) might become useless.

Related GitHub Issues: None.

[sc-57982]

[github-actions]

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Please edit doc/releases/changelog-dev.md with:

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.47%. Comparing base (29f1d90) to head (853d0d1).

Additional details and impacted files

@@            Coverage Diff             @@
##           ham-tests    #5415   +/-   ##
==========================================
  Coverage      99.47%   99.47%           
==========================================
  Files            400      400           
  Lines          37146    37143    -3     
==========================================
- Hits           36950    36949    -1     
+ Misses           196      194    -2     

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[Qottmann]

I think we can have best of both worlds with the suggestion. Else looks great 👍 Happy to approve with that fixed :)

[lillian542]

I think one pair of legacy and new tests can be combined now, but no blocking comments. Looks good to me, glad this is resolved! 🚀

[Qottmann]

nice 👌