(fix): add convert_strings_to_categoricals to methods

[flying-sheep]

• Closes Clarify export status of anndata.io.write_* functions #1915
• Tests added
• Release note added (or unnecessary)

Also

• fixes the Path types all over.
• Exports anndata.io.write_{h5ad,zarr} in an understated manner

I added this to the 0.11.4 milestone as it mostly corrects an oversight in #1474, but if you want I can split this up instead.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 80.53%. Comparing base (45b796f) to head (591808e).
Report is 49 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1914      +/-   ##
==========================================
- Coverage   82.81%   80.53%   -2.28%     
==========================================
  Files          45       45              
  Lines        6774     6777       +3     
==========================================
- Hits         5610     5458     -152     
- Misses       1164     1319     +155     

Files with missing lines	Coverage Δ
src/anndata/_core/anndata.py	82.51% <100.00%> (+0.04%)	⬆️
src/anndata/_core/file_backing.py	88.69% <100.00%> (ø)
src/anndata/_io/h5ad.py	92.68% <100.00%> (ø)
src/anndata/_io/read.py	81.48% <100.00%> (ø)
src/anndata/_io/specs/methods.py	84.27% <ø> (-1.47%)	⬇️
src/anndata/_io/write.py	77.77% <100.00%> (ø)
src/anndata/_io/zarr.py	82.02% <100.00%> (ø)
src/anndata/experimental/backed/_io.py	38.88% <100.00%> (+1.15%)	⬆️
src/anndata/experimental/merge.py	86.72% <100.00%> (ø)

... and 7 files with indirect coverage changes

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[ilan-gold]

fixes #1850 as well

[ilan-gold]

Definitely an oversight on the API's part, feel free to make a release