Consistently using PathInput and Path in both APIs

[forman]

Summary

Renames the public TypeScript path input type from PathLike to PathInput, adds PathSegmentInput, and mirrors the same input-type vocabulary in Python.

Also moves Python path normalization into remotestate.path as public helpers:

• normalize_path(path: PathInput) -> Path
• normalize_path_segment(segment: PathSegmentInput) -> PathSegment

Store now uses these public path normalization helpers instead of private PathKey aliases.

Changes

• Added Python PathInput and PathSegmentInput aliases.
• Added Python normalize_path() and normalize_path_segment().
• Replaced Python Store’s private PathKey / PathKeySegment typing with PathInput.
• Renamed TypeScript PathLike to PathInput.
• Added TypeScript PathSegmentInput.
• Updated React hook type annotations and exports.
• Updated README and CHANGES.md in both packages.
• Added focused tests for the new public path input names.

Checklists

Python package

• pixi run format
• pixi run lint
• pixi run mypy
• pixi run tests
• Updated remotestate-py/CHANGES.md

TypeScript library

• npm run format
• npm run checks
• npm run tests
• npm run build
• Updated remotestate-ts/CHANGES.md

Demo app

• npm run checks
• npm run build
• Updated remotestate-demo/CHANGES.md

[forman]

ok