Fix unread channel badge state

[wesbillman]

Summary

• fix unread channel persistence so read state is rehydrated per user without being overwritten on channel refresh or reopen
• make channel unread activity and the app icon badge follow unread/read state instead of unrelated home-feed counts or non-readable channel events
• stabilize relay-backed and smoke unread coverage, including reopen persistence and shortcut timing in related desktop integration tests

Verification

• cargo test -p sprout-db channel_activity_kinds
• cd desktop && pnpm check
• cd desktop && pnpm build
• cd desktop && pnpm exec playwright test --project=smoke
• cd desktop && pnpm exec playwright test --project=integration
• pre-push hook passed: rust fmt, desktop check, desktop tauri check, rust clippy, unit tests, desktop build