Cache sidebar content for instant render on subsequent launches

[ratley]

What Changed

Caches the sidebar project & thread titles.

Why

The sidebar currently doesn't render anything until the WebSocket is connected, resulting in "No projects yet" being shown for a couple of seconds when the app is opened. This is a UX improvement.

UI Changes

Before

t3-sidebar-before.mov

After

t3-sidebar-after.mov

Checklist

• This PR is small and focused
• I explained what changed and why
• I included before/after screenshots for any UI changes
• I included a video for animation/interaction changes

Note

Cache sidebar projects and threads in localStorage for instant render on subsequent launches

• readPersistedState in store.ts now parses cachedProjects and cachedThreads from localStorage and hydrates state.projects and state.threads on startup, with threadsHydrated: false until the server response arrives.
• persistState now writes cachedProjects and cachedThreads to localStorage on each state update, expanding the storage schema.
• Behavioral Change: on first load after this change, the sidebar renders from cache immediately rather than waiting for server data; stale cache is replaced once syncServerReadModel completes.

^{Macroscope summarized a15da82.}

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