polish(projects): streamline overview navigation and state

[thomaspblock]

Summary

• make the Projects overview follow the active section with consistent context, empty states, and row alignment
• add an animated section-local search that preserves sort and responsive tab behavior
• simplify sidebar and list controls while keeping large project collections incrementally mounted

This is Part 6 of the channel-first Projects stack, based on #6597. The final part contains project workspace aggregation and the default project-home template.

Testing

• focused search, activity digest, agent selection, related-channel, and overview-context tests: 26/26 passed
• Desktop unit suite: 5,451/5,451 passed
• E2E-mode Desktop build passed
• TypeScript, Biome, and differential file-size checks passed
• full pre-push gate passed

Post-Deploy Monitoring & Validation

• exercise every Projects overview section, search transition, selection state, and right context rail in staging Desktop
• healthy signals: stable tabs, aligned rows, correct section context, and responsive large-list interaction
• failure signals: search flicker, stale context, wrapped toolbar rows, missing empty actions, or input lag; mitigate by reverting this PR