feat(tui): add adaptive session tabs

[kitlangton]

What

Adds opt-in persistent session tabs to the TUI while preserving pinned sessions as the default navigation mode.

• Enabling Settings > Session > Tabs replaces pinned quick slots with tab navigation and restores pins unchanged when disabled.
• The strip remains visible with one real session. The existing new-session action navigates home without creating a synthetic tab; the first prompt creates and selects the real session tab.
• Roomy tabs share width equally up to 32 cells. Under pressure, inactive tabs contract evenly toward 8 cells while the active tab receives the remaining width. A sticky overflow window takes over when needed.
• Active, unread, attention, error, running, and idle states use distinct semantic treatments without status glyphs.
• Running sweeps fade from their current phase on completion while a fast-attack, slow-decay accent background pulse is composited over them. Completion orange remains suppressed until the entire root-session family has no running or pending work.

How

• context/session-tabs.tsx owns the real root-session working set, unread state, family activity, navigation, deletion reconciliation, and serialized persistence writes. Failed writes do not advance the persisted snapshot, so a later save can retry them.
• context/session-tabs-model.ts contains the pure open, close, cycle, sticky-window, and adaptive-width rules.
• component/session-tabs.tsx coordinates adaptive geometry, cached family status, state transitions, terminal-width title fading, and overlaid hover actions for real sessions.
• ui/animation.ts gives numeric objects and arrays one lazy shared scheduler with spring and tween retargeting, disabled-animation snapping, and per-animation timing. The existing prompt metadata fade uses the same scheduler.
• component/tab-pulse.tsx uses OpenTUI's shared render frame. Inactive pulse renderables are not live; running, fade-out, and completion channels share one compositing pass.
• Mutually exclusive keymap layers prevent tab shortcuts from colliding with pinned-session quick slots.

Persistence

Real tabs and unread state are stored in the TUI global state directory as session-tabs.json.

Each TUI reads the global snapshot at startup and then owns process-local state. Running terminals do not live-sync, so concurrent writers are currently last-writer-wins. This PR does not claim project-scoped or synchronized tab workspaces; if cross-terminal sharing is desired, that state should become service-owned rather than adding more client-side file coordination.

Scope

• Tabs remain disabled by default for compatibility with existing pinned-session behavior.
• This does not add service, protocol, or database state.
• This does not preserve transcript scroll position per tab; session routes retain their existing bottom-on-entry behavior.
• This does not change Warp's interception of Ctrl+Tab; leader-arrow bindings remain available.

Testing

• bun run test from packages/tui: 562 passed, 5 skipped, 0 failed.
• bun typecheck from packages/tui: passed.
• Push hook: all 33 workspace typecheck tasks passed.
• Live PTY verification against the V2 service at compact and roomy widths.
• Verified tab/pin mode switching, one-session visibility, sticky overflow, selection transitions, and resize stability.

Demo

Real-session route with one-space rail-less tab spacing:

Flow

flowchart LR
  Settings{Session tabs enabled?}
  Pins[Pinned session picker]
  Sessions[Persisted real tabs]
  Home[New session screen]
  Created[First prompt creates session]

  Settings -- No --> Pins
  Settings -- Yes --> Sessions
  Sessions -- New session action --> Home
  Home -- Submit first prompt --> Created
  Created -- Add real tab --> Sessions

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