fix(desktop): refetch home feed immediately on live mentions

[wesbillman]

Summary

• refetch the Home feed immediately when the existing live unread-message websocket stream receives an @mention for the current user
• keep workflow approvals and other Home needs-action items on the existing poll path for now
• add integration coverage that proves the Home badge and desktop notification update once without duplicate alerts after the follow-up Home refetch

Testing

• cd desktop && pnpm typecheck
• cd desktop && pnpm check
• cd desktop && pnpm test:e2e:integration --grep "live mentions refetch the home feed without waiting for polling"
• pre-push hook: cargo fmt --all -- --check
• pre-push hook: cargo fmt --manifest-path desktop/src-tauri/Cargo.toml --all -- --check
• pre-push hook: cd desktop && pnpm check
• pre-push hook: cd desktop && pnpm build
• pre-push hook: cargo check --manifest-path desktop/src-tauri/Cargo.toml
• pre-push hook: cargo clippy --workspace --all-targets -- -D warnings
• pre-push hook: ./scripts/run-tests.sh unit

[wesbillman]

@codex please review

[chatgpt-codex-connector]

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[chatgpt-codex-connector]

Avoid resubscribing mention streams on every channel update

mentionChannelIds is derived from the full channels array and then used as a useEffect dependency for mention subscriptions. Because channels is updated on each incoming message (via updateChannelLastMessageAt), this array gets a new identity even when the channel IDs are unchanged, so the effect tears down and recreates all mention subscriptions repeatedly. In active workspaces this creates avoidable subscription churn and short unsubscribe windows where live mentions can be missed until polling catches up.

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