Make the new-chat project heading interactive

[yaacovcorcos]

User impact

• The empty New Chat heading now reads What should we do in <Project>?, with the project name acting as an accessible project-picker trigger.
• Selecting another project moves the unsent draft through Scient's existing project-selection path without changing the route.
• Heading navigation and the nested command retain distinct accessible names before and after selection.

Upstream provenance and disposition

• Synara donor: 2c237bfb887b574076fd5a80927655f324c59009 (with later styling context from afc69fb3 and e89af583).
• Disposition: Adapt. The interaction concept is implemented through Scient's existing ProjectPicker and draft move/create/reset handlers; donor project/worktree assumptions are not imported.

Verification

• Focused browser acceptance verifies heading and button accessible names, project/draft state, environment reset, and stable route.
• Full stable browser suite passed: 58 files, 353 tests passed, 19 skipped.
• bun run scient:upstream-check --intake: identity, format, lint, typecheck, full bun run test, desktop/web builds, and release smoke all passed at 0069a20ff649fc7df7064b3a2d93d1f593dc7916.
• git diff --check; clean worktree; tests created no tracked artifacts.
• One P3 accessibility finding was fixed; exactly three independent read-only recertifications then found no P0-P3 issues.

Safety and rollback

• Reuses existing authority and state transitions; no persistence, provider, credentials, migration, updater, packaging, or shared-contract change.
• Rollback is a two-commit PR revert.
• No visual snapshot or manual computer-use validation was performed; interaction and accessibility are covered by code-level browser tests.

Related intake PRs

• Crash-loop breaker: Bound repeated desktop backend crash restarts #126
• Diff/Git refresh: Keep diff mode and Git status refresh responsive #127
• Migration lineage guard: Guard released migration lineage and dependencies #129
• Parent recovery research record: ScientFactory/Scient#49

[yaacovcorcos]

Final integration refresh (2026-07-25): current main dab9b6d was merged normally into this branch; no rebase or force-push. Exact hosted head: ea5a423. The local full-file browser run passed 81/82 and hit one ResizeObserver timing miss in an unrelated geometry case; that exact case passed in isolation, and the fresh hosted stable-browser plus Linux-geometry suites passed completely. git diff --check passes and the task worktree is clean. Fresh hosted CI run https://github.com/ScientFactory/scient-desktop/actions/runs/30160244171 completed successfully, including format, lint, typecheck, full bun run test, stable browser, Linux geometry, desktop build/preload, release smoke, Linux and Windows HTML-preview smoke, and Windows process regression. No unresolved review threads remain. Existing documented manual limitations are unchanged and non-blocking. This candidate is integration-ready against main dab9b6d; this is not merge or release authorization.