feat(tasks): TUI task board

Add a cross-project task board to the TUI (T / palette): a roster fetched
from GET /tasks with vim-style nav, refresh, and an enter-to-open detail
pane (goal, criteria, paths, links, notes) built from the list payload — no
extra fetch. Server: TaskService.listAll() and a project-optional GET /tasks
(scoped with ?project=, whole board without; recent-first).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

apps/tui-go/internal/app/update.go

@@ -116,6 +116,10 @@ func (m Model) Update(msg tea.Msg) (tea.Model, tea.Cmd) {
 		}
 		return m, nil
 
+	case tasksLoadedMsg:
+		m.applyTasksLoaded(msg)
+		return m, nil
+
 	case tea.KeyPressMsg:
 		next, cmd := m.handleKey(toKeyMsg(msg))
 		// A keypress may have entered a typing/active state (insert mode, steering, …);
@@ -300,6 +304,9 @@ func (m Model) handleNormalKey(k keyMsg) (tea.Model, tea.Cmd) {
 		// Resume browser: recent sessions over HTTP, reachable even after a server
 		// restart + TUI reopen (the live stream only carries running sessions).
 		return m, m.openSessions()
+	case "T":
+		// Task board: all tasks across projects over HTTP (GET /tasks).
+		return m, m.openTasks()
 	case "S":
 		m.openStats()
 	case "G":
@@ -641,6 +648,11 @@ func (m Model) handleOverlayKey(k keyMsg) (tea.Model, tea.Cmd) {
 	if m.overlay == OverlaySessions {
 		return m.handleSessionsKey(k)
 	}
+	// Tasks overlay owns all its keys: r refresh emits a cmd and enter toggles a detail
+	// pane, so it can't share the generic no-cmd esc path below.
+	if m.overlay == OverlayTasks {
+		return m.handleTasksKey(k)
+	}
 	if k.Type == keyEsc {
 		// In the event inspector, esc first stops an in-progress filter edit (keeping the
 		// query) rather than closing the overlay.
@@ -1095,6 +1107,7 @@ func paletteCommands() []paletteCmd {
 		{"artifacts", "v", "view artifacts", "browse this session's artifacts"},
 		{"stats", "S", "session stats", "metrics for the selected session"},
 		{"sessions", "R", "resume session", "browse / resume recent sessions"},
+		{"tasks", "T", "task board", "browse tasks across projects"},
 		{"config", "g", "edit config", "view / change correx settings"},
 		{"grants", "G", "grants", "view / revoke standing grants"},
 		{"statusbar", "", "status bar", "show / hide status-bar segments"},
@@ -1141,6 +1154,8 @@ func (m Model) execPalette(id string) (tea.Model, tea.Cmd) {
 		m.openStats()
 	case "sessions":
 		return m, m.openSessions()
+	case "tasks":
+		return m, m.openTasks()
 	case "config":
 		m.openConfig()
 	case "grants":