fix(browse): keep filters when switching sections

[oldreceipt]

Switching between Mods, Sounds, and WiPs clears the selected hero and category. Keep the hero across tabs and remember each section's category for the current session. Sounds' "No hero" option stays specific to Sounds.

Update the section and its filters together in the store so category requests cannot erase a newer selection. Remote fallback searches for heroes by name on Sounds and WiPs, since their category IDs differ from Mods.

Verified on Windows:

• All 11 focused filter tests passed.
• Full suite with fix(tests): make the full suite portable across hosts #428 applied: 183 files passed, 2,714 tests passed, one existing skip.
• Typecheck, lint, UI conventions, and i18n checks passed.
• Production build and Windows packaging passed. A local test build was provided before opening this PR.