refactor(nexus): add BuilderTabStrip to ProjectDetail (phase 11)

Integrates the Phase 11 Builder tab strip into ProjectDetail without
disturbing any existing Paperclip sub-route behavior. The approach:

1. When location.pathname resolves to a Builder tab (overview /
   issues / agents / gates / costs / activity / org), render the
   BuilderTabStrip + the matching new tab component (OverviewTab /
   ProjectIssuesList / AgentsTab / etc.) and hide the legacy
   PageTabBar + legacy overview/list handlers.
2. When the pathname resolves to a legacy tab (configuration /
   budget / workspaces / plugin:*), the existing Tabs/PageTabBar and
   dispatch render exactly as before — backwards compat preserved.

This is Option 1 from the Phase 11 plan: union the old and new tab
logic, silent pass-through for configuration/budget, no surface in
the new strip.

OverviewTab currently receives null for every data slice
(progress/milestones/originChat/activity24h) because the shared
Project type + projectsApi don't carry those fields yet; the tab
renders explicit em-dash / "No milestones defined" placeholders.
See the Phase 11 report for the backend gap list.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

ui/src/pages/ProjectDetail.tsx

@@ -24,6 +24,13 @@ import { ExecutionWorkspaceCloseDialog } from "../components/ExecutionWorkspaceC
 import { IssuesList } from "../components/IssuesList";
 import { PageSkeleton } from "../components/PageSkeleton";
 import { PageTabBar } from "../components/PageTabBar";
+import { BuilderTabStrip, resolveBuilderTab } from "../components/projects/BuilderTabStrip";
+import { OverviewTab } from "../components/projects/tabs/OverviewTab";
+import { AgentsTab } from "../components/projects/tabs/AgentsTab";
+import { GatesTab } from "../components/projects/tabs/GatesTab";
+import { CostsTab } from "../components/projects/tabs/CostsTab";
+import { ActivityTab } from "../components/projects/tabs/ActivityTab";
+import { OrgTab } from "../components/projects/tabs/OrgTab";
 import { buildProjectWorkspaceSummaries } from "../lib/project-workspaces-tab";
 import { projectRouteRef, projectWorkspaceUrl } from "../lib/utils";
 import { timeAgo } from "../lib/timeAgo";
@@ -847,6 +854,63 @@ export function ProjectDetail() {
         itemClassName="inline-flex"
       />
 
+      {/*
+        Phase 11 Builder tab strip. Renders iff the current URL resolves
+        to one of the new Builder tabs (overview/issues/agents/gates/
+        costs/activity/org). Legacy sub-routes (configuration/budget/
+        workspaces/plugin) fall through to the existing PageTabBar
+        below for backwards compat — see plan §Preserving existing
+        behavior.
+      */}
+      {(() => {
+        const builderTab = resolveBuilderTab(location.pathname, canonicalProjectRef);
+        if (!builderTab) return null;
+        // Phase 11: no reliable per-project agent count source yet. Show
+        // the full (7-tab) strip by default; BuilderTabStrip hides ORG
+        // when hasMultipleAgents=false. Leaving this true preserves
+        // access to the Org placeholder tab until the data is wired.
+        const hasMultipleAgents = true;
+        return (
+          <div data-testid="project-detail-builder-chrome" className="space-y-6">
+            <BuilderTabStrip
+              projectRef={canonicalProjectRef}
+              activeTab={builderTab}
+              hasMultipleAgents={hasMultipleAgents}
+            />
+            {builderTab === "overview" && (
+              <OverviewTab
+                project={{ name: project.name, status: project.status }}
+                progress={null}
+                activeAgentsCount={0}
+                milestones={null}
+                originChat={null}
+                activity24h={{
+                  commits: null,
+                  issuesClosed: null,
+                  gatesAwaiting: null,
+                  costBurnedCents: null,
+                }}
+              />
+            )}
+            {builderTab === "issues" && project?.id && resolvedCompanyId && (
+              <ProjectIssuesList projectId={project.id} companyId={resolvedCompanyId} />
+            )}
+            {builderTab === "agents" && <AgentsTab projectId={project.id} />}
+            {builderTab === "gates" && <GatesTab projectId={project.id} />}
+            {builderTab === "costs" && <CostsTab projectId={project.id} />}
+            {builderTab === "activity" && <ActivityTab projectId={project.id} />}
+            {builderTab === "org" && <OrgTab projectId={project.id} />}
+          </div>
+        );
+      })()}
+
+      {/*
+        Legacy Paperclip chrome — rendered only when the current tab is
+        NOT a Builder tab (configuration / budget / workspaces / plugin).
+        This preserves existing behavior for every pre-Phase-11
+        sub-route while the Builder strip owns the new tabs.
+      */}
+      {resolveBuilderTab(location.pathname, canonicalProjectRef) === null && (
       <Tabs value={activeTab ?? "list"} onValueChange={(value) => handleTabChange(value as ProjectTab)}>
         <PageTabBar
           items={[
@@ -865,8 +929,9 @@ export function ProjectDetail() {
           onValueChange={(value) => handleTabChange(value as ProjectTab)}
         />
       </Tabs>
+      )}
 
-      {activeTab === "overview" && (
+      {activeTab === "overview" && resolveBuilderTab(location.pathname, canonicalProjectRef) === null && (
         <OverviewContent
           project={project}
           onUpdate={(data) => updateProject.mutate(data)}
@@ -877,7 +942,7 @@ export function ProjectDetail() {
         />
       )}
 
-      {activeTab === "list" && project?.id && resolvedCompanyId && (
+      {activeTab === "list" && project?.id && resolvedCompanyId && resolveBuilderTab(location.pathname, canonicalProjectRef) === null && (
         <ProjectIssuesList projectId={project.id} companyId={resolvedCompanyId} />
       )}