TYP: widen duplicated() input type to AnyArrayLike (GH 42604)

[gkneighb]

• closes TYP: Improve typing on pandas.core.algorithms.duplicated() #42604
• Tests added and passed — N/A (type-only change; existing tests for test_algos.py and Series duplicated/drop_duplicates continue to pass)
• All code checks passed (ruff lint+format, mypy, pyright — 0 new findings on the modified file).
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/vX.X.X.rst file — omitted, following the convention of recent internal TYP PRs (e.g. TYP: typing for IndexSlice #65465, TYP: fix frame apply reduction typing #65555, TYP: type-check pandas.core.sample #65533, TYP: annotate pandas/_config/config.py #65549) which did not add whatsnew entries.
• I have reviewed and followed all the contribution guidelines.
• If I used AI to develop this pull request, I prompted it to follow AGENTS.md.

Summary

pandas.core.algorithms.duplicated() already accepts Series and Index at runtime (its internal call to _ensure_data unwraps them via extract_array), and its user-facing docs reflected this since #41985. Only the type annotation and docstring lagged behind. This widens both duplicated() and _ensure_data() from ArrayLike to AnyArrayLike (which adds Index | Series) and updates the parameter docstrings to match.

Widening a parameter type is backward-compatible — existing callers passing ArrayLike continue to type-check unchanged.

Note

This PR was developed with AI assistance (Claude); the agent was given AGENTS.md as guidance.