fix(app): load sidebar sessions after project restore

[SpencerJung]

Summary

• reload project session lists after persisted projects are restored instead of only on the initial mount
• ensure web server mode still creates the child stores required to fetch sidebar sessions when project hydration happens after startup
• keep the fix scoped to the app layout bootstrap path for Web UI: session list empty on left panel when using web server mode #27837

Why

In web server mode, the sidebar can stay empty when the saved project list is restored after the original one-time session bootstrap has already run. Moving the bootstrap behind reactive readiness means the session list is fetched once persisted projects are actually available.

Verification

• lsp_diagnostics packages/app/src/context/layout.tsx
• �un test --preload ./happydom.ts ./src/context/layout.test.ts
• �un run build
• �un run typecheck (fails on existing packages/app/src/custom-elements.d.ts parse error: ../../ui/src/custom-elements.d.ts)

Fixes #27837