Build the phone's navigation shell and sessions home

What this does

The phone's shell after the agreed mockups (docs/ui-prototypes/mobile/01-home-and-session.html, 04 for inbox and search):

• Floating pill nav as the tab bar. Sessions · Inbox · Settings are an expo-router Tabs group (src/app/(tabs)/) whose tab bar is the glass pill, with search detached beside it. Each tab is one instance that keeps its own state and scroll. A tap goes through the navigator (tabPress, then navigate), so switching never stacks screens, re-tapping does nothing, and Android back goes to Sessions and then out. The Inbox badge counts the sessions waiting on you, and screen readers hear it too ("Inbox, 2 need you").
• Sessions home. Big title with the environment line (live dot, label, route kind) and tabs All · Active · Drafts. Active is grouped as Needs you · Working · Failed · Recent, and empty groups are left out. All is grouped by day (Today, Yesterday, weekday, "Earlier this month", then the month). A tree is ranked by its most urgent member and dated by its newest one, so live work in a child is never buried under a quiet parent. A child session nests under its parent with a connector. Each row shows one status glyph per state, then the title, project chip, what the session is doing, and its age. A draft row shows the first line, the project, the tool as its mark (never its name), the image count, and "Not synced" or "Sending".
• Inbox. Needs you (Permissions / Questions / Plans) · Done · Failed, with an all-clear state. "Mark all seen" waits until it can acknowledge on the server.
• Search. A modal in the root stack, with the field and projects shown before you type. Matching is word-wise across title and project ("tool pay" finds "Tool Call Payloads"), and results show as the standard rows, then projects.
• Placeholders with working back controls. There is a session page frame, a "New session" page behind the compose button, and a draft page behind each draft row. Back and close return to the previous screen, or to the home when a cold deep link left nothing to go back to.

Design system (apps/mobile/src/ui)

• Glass: expo-blur under the scheme's translucent floating surface plus the float shadow, fed by the theme tokens.
• StatusMark: one glyph per state. The glyph ink comes from the theme: inkOn / statusInk pick the canvas or the ink by WCAG contrast.
• ProviderMark: the web provider marks.
• ProjectChip: a project's square, in a colour picked from the theme's documented project palette by the project's name.
• Rows and chrome: SessionRow, DraftRow, SegmentedTabs, BigTitle, SectionLabel, FadeOut, IconButton.

Fills, not borders. The home and inbox lists are SectionLists.

Data

The home reads through src/home/source.ts. Until the phone speaks the environment protocol, that returns a fixture (src/home/fixture.ts) in the shared sidebar's own shapes (SidebarSessionEntry, SidebarDraft, WorkspaceEntry). The sessions-list work swaps the hook for the shared sidebar providers without touching the screens.

Status marks use the web sidebar's own mapping. sessionBusyTone moved into a pure, import-free app-core module (packages/app-core/src/components/sidebar/session-busy-tone.ts). It is exported from the logic graph and as a package subpath, and SessionBusyLoader re-exports it, so web is unchanged. done, busy, ready and idle read the same on both, and a status with no glyph shows the ring at rest. Nothing here invents, merges or changes server state.

src/home/rows.ts and src/home/search.ts are pure and unit-tested.

Also

• Every screen paints the theme canvas, so the navigator's default white never shows.
• The Convex-era session page stays behind its provider when EXPO_PUBLIC_CONVEX_URL is set. Otherwise the page frame shows, so the app runs with no Convex at all.
• New native modules: expo-blur, expo-haptics, expo-linear-gradient (SDK-pinned).
• README: a Shell section.
• Android glass (a BlurView inside the BlurTargetView it blurs) still needs a check on a device.

Verification

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