Invalidate the tagged-mesh cache when the source file changes

[aabills]

Description

TaggedSubMeshGenerator caches parsed .msh files so a multi-domain model reading the same file for several regions parses it once. The cache was an unbounded, class-level dict keyed on the raw path object:

_mesh_cache: dict = {}

@classmethod
def _read(cls, path):
    if path not in cls._mesh_cache:
        cls._mesh_cache[path] = meshio.read(str(path))
    return cls._mesh_cache[path]

Three problems:

1. Never invalidated on file change. The key is just the path, so editing the .msh on disk and re-running in the same session silently returns the old mesh. This bites anyone iterating on a mesh during development — their edits are ignored until the process restarts.
2. Unbounded and process-global. A class attribute shared across all instances, never cleared; every file read stays in memory for the process lifetime.
3. str vs Path double-caches. The key is the raw object, so "x.msh" and Path("x.msh") create two entries for the same file.

Verified the stale read empirically: after rewriting a file from 9 to 18 points on disk, _read returned the same 9-point object.

Fix

Key on (os.fspath(path), st_mtime_ns) via functools.lru_cache:

• os.fspath collapses str/Path to one key,
• the modification time in the key makes an edited file a cache miss → re-read,
• lru_cache(maxsize=8) bounds retained meshes.

Testing

• New test test_tagged_generator_cache_reads_and_invalidates: same unchanged file returns the same object (cache hit), str/Path collapse to one entry, and bumping the file's mtime forces a re-read.
• The four existing test_tagged_generator_* tests injected fake meshes into _mesh_cache directly; they now monkeypatch _read (they test region extraction, not caching).
• uv run --group dev pytest packages/pybamm/tests/unit/test_meshes — 163 passed.
• uv run pre-commit run --all-files clean.

🤖 Generated with Claude Code

[aabills]

Closing: out of scope for #5688. Pre-existing item in already-merged #5687 mesh code, not part of the spatial-method PR.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.12%. Comparing base (f82976f) to head (6957fad).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #5705   +/-   ##
=======================================
  Coverage   98.11%   98.12%           
=======================================
  Files         340      340           
  Lines       32744    32748    +4     
=======================================
+ Hits        32128    32134    +6     
+ Misses        616      614    -2     

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