List a session's background tasks above its subagents

The count beside the status said how much work was going and never what,
so "3 bg tasks" was a number with no way to find out what it was about.

Drivers now report the tasks themselves rather than a size:
`Driver::background_tasks` returns `Vec<BackgroundTask>` -- id, the
provider's own description, and a kind -- served by
`GET /sessions/{id}/background`. It is runtime state, never persisted,
and `null` is "nobody has said", which is what a session with no process
answers and what the panel says in words rather than drawing as an empty
list. `description` is optional because Codex names a background terminal
by a process id, and a number drawn as a name is worse than admitting
there is none.

Claude's `background_tasks_changed` entries turn out to be objects
carrying `task_id`, `task_type` and `description`, so each is read rather
than counted -- and an `ambient` one is now dropped from the list and the
count alike, on the CLI's own instruction: a live-update watcher is not
activity, and counting one left a session reading `waiting` with nothing
to wait for.

The phone draws them in the right-hand panel above the subagents,
collapsed to "2 bg tasks running" and pushing the subagents down when
opened. Both lists are items of one lazy column, so neither can run off
the panel, and the section is refetched whenever the live count moves --
a card for work that has finished is exactly the stale measurement the
count exists not to be.

Verified against the real Claude CLI (2.1.261): a backgrounded `sleep 120`
came back as `{"id":"br16327wr","description":"Sleep for 120 seconds",
"kind":"command"}`, and on the emulator against the echo rig the section
appeared, expanded, and dropped a card as its task finished.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

app/androidApp/src/main/kotlin/com/example/aiapp/BackgroundTasks.kt

@@ -0,0 +1,155 @@
+package com.example.aiapp
+
+import androidx.compose.foundation.clickable
+import androidx.compose.foundation.layout.Column
+import androidx.compose.foundation.layout.Row
+import androidx.compose.foundation.layout.Spacer
+import androidx.compose.foundation.layout.fillMaxWidth
+import androidx.compose.foundation.layout.height
+import androidx.compose.foundation.layout.heightIn
+import androidx.compose.foundation.layout.padding
+import androidx.compose.foundation.layout.width
+import androidx.compose.foundation.lazy.LazyListScope
+import androidx.compose.material3.CircularProgressIndicator
+import androidx.compose.material3.LocalContentColor
+import androidx.compose.material3.MaterialTheme
+import androidx.compose.material3.OutlinedCard
+import androidx.compose.material3.Text
+import androidx.compose.material3.TextButton
+import androidx.compose.runtime.Composable
+import androidx.compose.ui.Alignment
+import androidx.compose.ui.Modifier
+import androidx.compose.ui.unit.dp
+
+/**
+ * The background work a session has going, above its subagents in the panel [SidePanels] slides
+ * over it from the right.
+ *
+ * Collapsed to its one-line count by default, the way everything else this app adds to a screen
+ * arrives: what a reader came to the panel for is the subagents, and a run of cards about work
+ * nobody asked after would push them off it. Expanding pushes them down instead of covering them,
+ * so the two are read together.
+ *
+ * Nothing is drawn at all when the count is zero -- including when the provider never said, which
+ * is the same absence the status row draws. A permanently visible "0 bg tasks" would be a line
+ * about nothing on every session that has never backgrounded anything, which is most of them.
+ */
+fun LazyListScope.backgroundTaskSection(
+    count: Int,
+    tasks: LoadState<List<BackgroundTaskSummary>?>,
+    expanded: Boolean,
+    onToggle: () -> Unit,
+    onRetry: () -> Unit,
+) {
+    if (count == 0) return
+    item(key = "background-heading") {
+        Row(
+            verticalAlignment = Alignment.CenterVertically,
+            modifier = Modifier.fillMaxWidth().heightIn(min = 48.dp).clickable(onClick = onToggle),
+        ) {
+            Text(
+                "${backgroundTaskLabel(count)} running",
+                style = MaterialTheme.typography.titleMedium,
+                modifier = Modifier.weight(1f),
+            )
+            Chevron(if (expanded) Pointing.Up else Pointing.Down)
+        }
+    }
+    if (!expanded) return
+    when (tasks) {
+        is LoadState.Loading ->
+            item(key = "background-loading") {
+                CircularProgressIndicator(modifier = Modifier.width(24.dp).height(24.dp))
+            }
+        is LoadState.Error ->
+            item(key = "background-error") {
+                Column {
+                    Text(
+                        tasks.message,
+                        color = MaterialTheme.colorScheme.error,
+                        style = MaterialTheme.typography.bodySmall,
+                    )
+                    TextButton(onClick = onRetry) { Text("Try again") }
+                }
+            }
+        // Null is the provider declining to say, which a session whose process has gone answers.
+        // Said in words: the count above came from somewhere, and an empty space under it would
+        // read as the tasks having finished rather than as nobody being left to ask.
+        is LoadState.Loaded ->
+            when (val rows = tasks.value) {
+                null ->
+                    item(key = "background-unknown") {
+                        Text(
+                            "This session isn't saying what these are.",
+                            color = MaterialTheme.colorScheme.onSurfaceVariant,
+                            style = MaterialTheme.typography.bodyMedium,
+                        )
+                    }
+                else ->
+                    uniqueItems(rows, key = { "background-${it.id}" }) { BackgroundTaskCard(it) }
+            }
+    }
+}
+
+/**
+ * One background task: what it is doing, and what kind of thing is doing it.
+ *
+ * Not something to open, unlike the subagent cards below it -- a task is a provider's runtime state
+ * and has no transcript of its own. A backgrounded agent that does is also in the subagent list,
+ * under its own name.
+ */
+@Composable
+private fun BackgroundTaskCard(task: BackgroundTaskSummary) {
+    val kind = backgroundTaskKindLabel(task.kind)
+    OutlinedCard(Modifier.fillMaxWidth()) {
+        Column(Modifier.padding(horizontal = 12.dp, vertical = 8.dp)) {
+            // The kind stands in as the title where the provider gave no description, rather than
+            // the id it named the task by: Codex reports a process number, which says nothing to
+            // the person reading and would look like a name somebody chose.
+            Text(
+                task.description ?: kind,
+                style = MaterialTheme.typography.titleSmall,
+                color =
+                    if (task.description == null) MaterialTheme.colorScheme.onSurfaceVariant
+                    else LocalContentColor.current,
+            )
+            if (task.description != null) {
+                Spacer(Modifier.height(2.dp))
+                Text(
+                    kind,
+                    style = MaterialTheme.typography.bodySmall,
+                    color = MaterialTheme.colorScheme.onSurfaceVariant,
+                )
+            }
+        }
+    }
+}
+
+/**
+ * What a [BackgroundTaskSummary.kind] is called on screen.
+ *
+ * A kind this build has not heard of is named by what every one of them has in common rather than
+ * by the nearest word we do know, which would be this screen asserting something the server never
+ * said.
+ */
+private fun backgroundTaskKindLabel(kind: String) =
+    when (kind) {
+        "agent" -> "subagent"
+        "command" -> "background command"
+        "workflow" -> "workflow"
+        else -> "background task"
+    }
+
+/**
+ * The heading over one group in the panel, so neither list is a run of cards with no name.
+ *
+ * The same band as the background section's own heading row above, rather than a gap chosen to look
+ * right here: what separates a heading from the cards above it is that both headings sit in a row
+ * of one height.
+ */
+@Composable
+fun PanelSectionHeading(text: String) {
+    Row(verticalAlignment = Alignment.CenterVertically, modifier = Modifier.heightIn(min = 48.dp)) {
+        Text(text, style = MaterialTheme.typography.titleMedium)
+    }
+}