chore(studio): track project-mode unification

[christso]

Objective

Converge Studio onto a single project-scoped architecture so "single-project mode" becomes a UI presentation choice, not a separate routing/data path.

Why

• PR fix(studio): scope experiment detail pages to project #1251 fixed a bug caused by drift between unscoped single-project experiment detail pages and project-scoped multi-project pages.
• The current split makes routes, navigation, breadcrumbs, and data fetching easy to diverge.
• Phoenix-style behavior is the target: when one project exists, auto-focus it; when many exist, show project selection; underneath, use the same project-scoped pages.

Proposed approach

1. Make project-scoped routes the canonical Studio routes for runs, experiments, analytics, targets, and drill-down pages.
2. Treat the current unscoped home as a thin redirect/selection layer:
   • 0 projects: onboarding/empty state
   • 1 project: automatically land on that project
   • many projects: show projects dashboard / picker
3. Move any remaining unscoped data loaders, links, sidebar logic, and breadcrumbs onto project-scoped equivalents.
4. Preserve current UX features; only remove duplicate mode-specific plumbing.
5. Add focused regression coverage for route/link generation so single-vs-multi drift cannot recur.

Acceptance signals

• Opening Studio with one registered project still gives a streamlined experience, without exposing broken or missing features.
• Opening Studio with many projects uses the same run/experiment/detail pages after a project is selected.
• No page fetches unscoped run/experiment data after a project has been selected.
• Sidebar, breadcrumbs, and deep links remain project-aware across runs, experiments, evals, analytics, and targets.
• Existing URLs either continue to work or redirect cleanly to project-scoped URLs.

Non-goals

• Redesigning Studio visuals
• Changing scoring or backend result semantics
• Reworking project registry behavior beyond what is needed to unify the UI flow

Suggested implementation order

1. Inventory remaining unscoped routes/components used after project selection.
2. Introduce redirect behavior from single-project entrypoints to the selected project.
3. Remove duplicate unscoped detail pages once project-scoped equivalents fully cover them.
4. Add regression tests for project-aware navigation and route generation.

Handoff notes

• Start from origin/main after PR fix(studio): scope experiment detail pages to project #1251.
• Use PR fix(studio): scope experiment detail pages to project #1251 as the concrete example of the drift this refactor should eliminate.
• Prefer deleting duplicated mode-specific code rather than layering more conditionals on top.

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