[ENH] Add capability:predict tag for Clustering

[TonyBagnall]

Motivation

many clusterers have no default use for fittting on unseen data (transducive clusterers). scikit simply has no predict method for these. We need to work it a bit more because of the predict/_predict model. This PR introduces a tag and tests for it in the base class. Needed for #3553

see #1241

What was changed:

• Tag registry (aeon/utils/tags/_tags.py): new capability:predict tag for the clusterer class — True means fit(X_train); predict(X_new) is supported; False means the clusterer is
  transductive and only fit(X)/labels_ and fit_predict(X) work.
• BaseClusterer (aeon/clustering/base.py): defaults "capability:predict": True so every existing clusterer is unaffected. predict and predict_proba now call a
  _check_predict_capability() helper after the fitted-state check and raise NotImplementedError with your suggested message when the tag is False. fit_predict now passes y through
  to fit and its docstring says it is equivalent to fitting on X and returning labels_ — it never touches predict. The fitted-state check deliberately runs before the capability
  check so unfitted estimators still raise the standard NotFittedError that common tests expect.
• Tests: new MockTransductiveCluster (its_predict raises RuntimeError if ever reached, proving fit_predict doesn't route through predict); MockCluster._fit now sets labels_ to
  match the base-class contract. test_base.py covers fit_predict/labels_ equivalence, fit_predict independence from _predict (via a call-counting clusterer), the error for tag-False
  clusterers, unchanged behaviour for tag-True ones, and the preserved NotFittedError. test_agglomerative.py keeps the PR's sklearn-equivalence tests and adds fit(X).labels_,
  fit_predict determinism, and the predict/predict_proba error tests.

Verification: the full check_estimator suite passes for TimeSeriesAgglomerative, DummyClusterer, and TimeSeriesKMeans; the whole clustering module (575 tests, deep learning
excluded), aeon/utils (556 tests), estimator-checking/mock tests (304), and the new class's docstring example all pass locally.

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I have added the following labels to this PR based on the title: [ enhancement ].
I would have added the following labels to this PR based on the changes made: [ clustering, testing ], however some package labels are already present.

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[TonyBagnall]

so my bot say this below and has rewritten the test, hopefully more to your liking, Are you ok with the actual changes @patrickzib? Its a design issue more than a testing style issue

Good questions, and you're right the test was loosely defined. The contract is that fit_predict(X) is fit(X) then return labels_, so it always refits — and for a non-deterministic clusterer (k-means being the obvious case) two separate fits need not agree, which is exactly why comparing two separate instances was fragile. I've rewritten it to test the contract directly on a single instance: fit_predict(X) returns labels_ from the fit it just performed, never predict(X). MockTransductiveCluster makes it discriminating — its labels_ are a known alternating 0/1 pattern and its predict raises, so matching that pattern shows fit_predict returned labels rather than routing through predict.

Agreed the _CountingClusterer was unnecessary. The property under test is the one documented on fit_predict: it must not route through _predict, so it stays valid for transductive clusterers. I've removed the counting clusterer and now test that directly with MockTransductiveCluster, whose _predict raises — fit_predict completing instead of erroring proves _predict was never called. That's the whole test now, with a docstring saying exactly that.

What changed in test_base.py

• test_fit_predict_returns_labels → rewritten as test_fit_predict_returns_labels_from_its_own_fit: tests the real contract on a single instance (returns labels_ from the fit it performs, not predict(X)), using
  the transductive mock's known 0/1 pattern as the discriminating check — no reliance on "two separate fits agree."
• test_fit_predict_does_not_call_predict → replaced by test_fit_predict_valid_without_predict_capability: _CountingClusterer deleted; now uses MockTransductiveCluster (whose _predict raises), so fit_predict
  completing proves _predict was never called.
• test_predict_without_capability_raises: matches only does not support out-of-sample prediction.
• Every test got a docstring explaining what it verifies; redundant import numpy.random removed.

[patrickzib]

Good questions, and you're right the test was loosely defined.

Agreed the _CountingClusterer was unnecessary.

Love it that agents are so affirmative :)

Thank you. I'll check again this afternoon.