feat(v0.6): auto-group Projects by namespace + Active-now band + cross-device prefs

The flat Projects grid was overwhelming at 50-100 repos. Explored the UX with
4 parallel agents (auto-grouping / manual folders / density-segmentation /
competitive research); all converged on namespace auto-grouping as the primary
fix — the dotted repo names (Billo.Platform.*, Billo.Infrastructure.*) already
encode the hierarchy, so it's a string-split, not a taxonomy the user builds.

Frontend:
- groupProjects(): depth-2 namespace grouping, >=2-member threshold (singletons
  fall to "Other"), degrade-to-flat when repos share no prefix, running projects
  duplicated into a pinned "Active now" section.
- displayLabel(): cards show the namespace tail (Payment, not
  Billo.Platform.Payment); full name in Active/Other.
- Collapsible sticky group headers with an "N active" badge so a collapsed
  section never hides running work; search force-expands matching groups.
- public/prefs.ts: server-first load with a localStorage offline mirror, migrates
  the legacy per-device proj-favs.

Backend (server-side prefs so favourites + collapse-state follow the user across
devices — localStorage was per-device, which broke the multi-device premise):
- src/http/prefs-store.ts: ~/.web-terminal-prefs.json store (mirrors push-store),
  every field bounded + sanitized.
- GET /prefs (read-only) + PUT /prefs (Origin-guarded); UiPrefs type +
  PREFS_STORE_PATH config.

Tests: +12 prefs-store, +21 groupProjects/displayLabel. Full suite 1227 passed.
Verified live: grouping renders, collapse persists to the server and survives a
full page reload (cross-device sync proven end-to-end).

test/projects-panel.test.ts

@@ -30,6 +30,10 @@ const {
   normalizeProject,
   makeProjectCard,
   renderProjectDetail,
+  groupProjects,
+  displayLabel,
+  ACTIVE_GROUP_KEY,
+  OTHER_GROUP_KEY,
 } = await import('../public/projects.js')
 
 /* ── Helpers ───────────────────────────────────────────────────────────────── */
@@ -509,3 +513,121 @@ describe('renderProjectDetail', () => {
     expect(h.onOpenProject).toHaveBeenCalledWith('/p/r', 'r', 'claude "/init"\r')
   })
 })
+
+/* ── groupProjects / displayLabel (namespace grouping, v0.6) ─────────────────── */
+
+const runningSession = { id: 's', status: 'working' as const, clientCount: 1, createdAt: 1, exited: false }
+
+function proj(name: string, over: Partial<ProjectInfo> = {}): ProjectInfo {
+  return makeProject({ name, path: `/repos/${name}`, ...over })
+}
+
+describe('groupProjects', () => {
+  const noFavs = new Set<string>()
+
+  it('groups repos sharing a two-segment namespace (≥2 members)', () => {
+    const groups = groupProjects(
+      [proj('Billo.Platform.Payment'), proj('Billo.Platform.Document')],
+      noFavs,
+    )
+    expect(groups).toHaveLength(1)
+    expect(groups[0].kind).toBe('namespace')
+    expect(groups[0].label).toBe('Billo.Platform')
+    expect(groups[0].projects.map((p) => p.name)).toEqual([
+      'Billo.Platform.Payment',
+      'Billo.Platform.Document',
+    ])
+  })
+
+  it('drops single-member namespaces and no-dot repos into "Other"', () => {
+    const groups = groupProjects(
+      [
+        proj('Billo.Platform.Payment'),
+        proj('Billo.Platform.Document'),
+        proj('Billo.Customer'), // lone "Billo.Customer" namespace
+        proj('web-terminal'), // no dot
+      ],
+      noFavs,
+    )
+    const other = groups.find((g) => g.kind === 'other')
+    expect(other).toBeDefined()
+    expect(other!.projects.map((p) => p.name).sort()).toEqual(['Billo.Customer', 'web-terminal'])
+  })
+
+  it('falls back to a single flat group when no namespace earns a section', () => {
+    const groups = groupProjects([proj('web-terminal'), proj('graphrag'), proj('piano')], noFavs)
+    expect(groups).toHaveLength(1)
+    expect(groups[0].kind).toBe('flat')
+    expect(groups[0].projects).toHaveLength(3)
+  })
+
+  it('pins an "Active now" section first with projects that have a running session', () => {
+    const groups = groupProjects(
+      [
+        proj('Billo.Platform.Payment', { sessions: [runningSession] }),
+        proj('Billo.Platform.Document'),
+      ],
+      noFavs,
+    )
+    expect(groups[0].kind).toBe('active')
+    expect(groups[0].label).toBe('Active now')
+    expect(groups[0].projects.map((p) => p.name)).toEqual(['Billo.Platform.Payment'])
+    // still also present inside its namespace group (deliberate duplication)
+    const ns = groups.find((g) => g.kind === 'namespace')!
+    expect(ns.projects.map((p) => p.name)).toContain('Billo.Platform.Payment')
+    expect(ns.activeCount).toBe(1)
+  })
+
+  it('orders namespace sections by their most-recently-active member', () => {
+    const groups = groupProjects(
+      [
+        proj('Old.Alpha.a', { lastActiveMs: 10 }),
+        proj('Old.Alpha.b', { lastActiveMs: 20 }),
+        proj('New.Beta.a', { lastActiveMs: 900 }),
+        proj('New.Beta.b', { lastActiveMs: 100 }),
+      ],
+      noFavs,
+    )
+    const ns = groups.filter((g) => g.kind === 'namespace').map((g) => g.label)
+    expect(ns).toEqual(['New.Beta', 'Old.Alpha'])
+  })
+
+  it('keeps "Other" last', () => {
+    const groups = groupProjects(
+      [proj('Billo.Platform.Payment'), proj('Billo.Platform.Document'), proj('loose')],
+      noFavs,
+    )
+    expect(groups[groups.length - 1].kind).toBe('other')
+  })
+
+  it('merges namespaces case-insensitively', () => {
+    const groups = groupProjects([proj('Billo.Platform.a'), proj('billo.platform.b')], noFavs)
+    expect(groups).toHaveLength(1)
+    expect(groups[0].projects).toHaveLength(2)
+  })
+
+  it('does not mutate the input array', () => {
+    const input = [proj('A.b.c'), proj('A.b.d')]
+    const copy = [...input]
+    groupProjects(input, noFavs)
+    expect(input).toEqual(copy)
+  })
+})
+
+describe('displayLabel', () => {
+  it('strips the namespace prefix inside a namespace group', () => {
+    expect(displayLabel('Billo.Platform.Payment', 'Billo.Platform')).toBe('Payment')
+    expect(displayLabel('Billo.Platform.Shared.DomainEvents', 'Billo.Platform')).toBe(
+      'Shared.DomainEvents',
+    )
+  })
+
+  it('shows the full name in the active and other sections', () => {
+    expect(displayLabel('Billo.Platform.Payment', ACTIVE_GROUP_KEY)).toBe('Billo.Platform.Payment')
+    expect(displayLabel('web-terminal', OTHER_GROUP_KEY)).toBe('web-terminal')
+  })
+
+  it('is case-insensitive on the prefix but preserves the tail casing', () => {
+    expect(displayLabel('Billo.Platform.Payment', 'billo.platform')).toBe('Payment')
+  })
+})