feat(app): show active project in session header

[TonisOrmisson]

Issue for this PR

Closes#43842

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

Shows the active project name in the conversation header, immediately before the existing context/cost control, so desktop users can identify the project while switching conversations.

The change stays intentionally small:

• Reuses the existing project and session directory state.
• Handles local and server-scoped session routes, including sandbox directories.
• Keeps the label truncated, RTL-safe, and aligned with the existing conversation-header actions.
• Does not add vertical tabs, a sidebar, project grouping, or conversation-title redesign.

Related context: #38143 and #38308. This PR is limited to the active-project visibility portion of #43842.

How did you verify your code works?

• bun run test from packages/app: 722 unit tests and 41 browser-condition tests passed.
• bun typecheck from packages/app passed.
• Verified desktop, mobile-width, and forced-RTL rendering with a deterministic Playwright session fixture.

Screenshots / recordings

Before:

After:

Mobile width:

Forced RTL:

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR

[Enough1122]

AI code review — automated review for reference; please use your judgment.

1. packages/app/src/components/session/session-header.tsx:158 — project switched from an explicit lookup (projects list matched against the resolved projectDirectory, including sandboxes) to plain sync().project. When viewing a session whose directory differs from the currently synced project (e.g., jumping into a historical/cross-project session via params.id), the header can now attribute it to the wrong project. Why it matters: the label is the primary orientation cue in the header. Suggestion: keep resolving project from the effective projectDirectory() first and use sync().project only as last-resort fallback.

2. packages/app/src/components/session/session-header.tsx:151-157 — the new fallback chain means a project name can render even when neither params.dir nor the session record yields a directory (projectDirectory === "" but sync().project set). If showing a name with no corresponding directory chip is intended, fine; otherwise gate the name on projectDirectory().

3. Test coverage — none of the new paths are covered: params.dir present, absent-with-session-directory, absent-without-session-directory, and empty-name suppression in SessionProjectName. Why it matters: this is exactly the kind of memo-fallback chain that silently breaks on refactor. Suggestion: add a component test driving params through those three cases.

4. Nit: packages/app/src/components/session/session-header.tsx:329 — in the non-V2 branch, SessionProjectName renders alongside the pre-existing xl: directory block; on wide screens the project may appear twice (once as name, once via the directory UI). Worth a quick visual check for redundancy.