Remove the qp.qaoa module

[JerryChen97]

Context:

Part of the ongoing removal of classic PennyLane modules for PennyLane2, following
the same pattern as qp.fourier (#10212), qp.noise (#10214), qp.qcut (#10235)
and qp.qnn (#10247).

Description of the Change:

Removes the pennylane.qaoa module:

• Deleted pennylane/qaoa/ (cost.py, cycle.py, layers.py, mixers.py, __init__.py)
  and tests/test_qaoa.py.
• Dropped from pennylane import qaoa from pennylane/__init__.py.
• Removed the pennylane.qaoa module block from tach.toml.
• Deleted doc/code/qp_qaoa.rst and its doc/index.rst toctree entry.
• Removed the --ignore=pennylane/qaoa rule from documentation-tests.yml.
• Added entries to doc/development/deprecations.rst and doc/releases/changelog-dev.md.

This covers the mixer Hamiltonians (x_mixer, xy_mixer, bit_flip_mixer), the cost
Hamiltonians (maxcut, max_independent_set, min_vertex_cover, max_clique,
max_weight_cycle, bit_driver, edge_driver), the ansatz layers (cost_layer,
mixer_layer) and the pennylane.qaoa.cycle helpers.

Deliberately left alone:

• QAOAEmbedding is a template under pennylane/templates/embeddings/, not part of this
  module, and is unaffected.
• rustworkx / networkx stay as dependencies; both are used elsewhere in the package.
• Unlike qp.qcut, qp.qaoa had no pytest marker, no dedicated CI job and no extras
  group, so there is nothing to remove from pytest.ini, conftest.py or pyproject.toml.

Benefits:

Less surface area to maintain and migrate to Operator2 / PennyLane2.

Possible Drawbacks:

Breaking change for anyone using qp.qaoa. There is no in-tree replacement.

Related GitHub Issues:
[sc-132149]

Authored with assistance from an AI coding assistant; all changes reviewed by a human.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.40%. Comparing base (a222dc9) to head (03d2491).

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #10249      +/-   ##
==========================================
- Coverage   99.41%   99.40%   -0.01%     
==========================================
  Files         603      598       -5     
  Lines       66975    66593     -382     
==========================================
- Hits        66580    66200     -380     
+ Misses        395      393       -2     

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[andrijapau]

What (if any) demos are affected by this?

[JerryChen97]

What (if any) demos are affected by this?

Searched PennyLaneAI/demos @ master. Five demos import the module directly:

Demo	APIs used
tutorial_qaoa_intro	edge_driver, min_vertex_cover, cost_layer, mixer_layer
tutorial_falqon	max_clique, cost_layer, mixer_layer
braket-parallel-gradients	maxcut, cost_layer, mixer_layer
learning2learn	maxcut, cost_layer, mixer_layer
qnspsa	maxcut, cost_layer, mixer_layer

[andrijapau]

What (if any) demos are affected by this?

Searched PennyLaneAI/demos @ master. Five demos import the module directly:
Demo APIs used
tutorial_qaoa_intro edge_driver, min_vertex_cover, cost_layer, mixer_layer
tutorial_falqon max_clique, cost_layer, mixer_layer
braket-parallel-gradients maxcut, cost_layer, mixer_layer
learning2learn maxcut, cost_layer, mixer_layer
qnspsa maxcut, cost_layer, mixer_layer

Can we add a story to this iteration to make sure we fix those?