Stop the sync poll from rebuilding the panel every 5 s

@Published fires even when the assigned value is unchanged, so the poll's
unconditional lastError = nil invalidated PanelView — which observes
SyncService — every 5 seconds, forever, hidden or visible. Over five days
that was ~185 CPU-minutes and ~190 MB, and clicks started to lag.

- Route poll state through setError, which skips equal values.
- Watch SyncService from a tiny SyncDot view instead of the panel body.
- Skip the URL cache on polls and give them timeouts.
- Only reassign the composer placeholder when it changed.

Sources/Prompt/SyncService.swift

@@ -193,13 +193,20 @@ final class SyncService: ObservableObject {
 
     private func poll() {
         guard !isSyncing, let code, let versionURL = endpoint("/api/sync/\(code)/version") else { return }
+        // A cached /version would keep reporting the version the client already
+        // has, so polls must always hit the network. The responses are a few
+        // bytes; letting CFNetwork write them to the disk cache every 5 s only
+        // adds churn.
+        var versionRequest = URLRequest(url: versionURL)
+        versionRequest.cachePolicy = .reloadIgnoringLocalCacheData
+        versionRequest.timeoutInterval = 15
         Task {
             do {
                 // Cheap poll first: the full payload can be megabytes of
                 // base64 images, so only download it when the version moved.
-                let (versionData, versionResponse) = try await URLSession.shared.data(from: versionURL)
+                let (versionData, versionResponse) = try await URLSession.shared.data(for: versionRequest)
                 if (versionResponse as? HTTPURLResponse)?.statusCode == 404 {
-                    lastError = "Sync group no longer exists on the server"
+                    setError("Sync group no longer exists on the server")
                     return
                 }
                 guard let versionHTTP = versionResponse as? HTTPURLResponse, versionHTTP.statusCode == 200 else {
@@ -208,12 +215,15 @@ final class SyncService: ObservableObject {
                 }
                 let remoteVersion = try JSONDecoder().decode([String: Int64].self, from: versionData)["version"] ?? 0
                 guard remoteVersion > lastVersion else {
-                    lastError = nil
+                    setError(nil)
                     return
                 }
                 syncLog("poll remote v\(remoteVersion) local v\(lastVersion) — fetching payload")
                 guard let payloadURL = endpoint("/api/sync/\(code)") else { return }
-                let (data, response) = try await URLSession.shared.data(from: payloadURL)
+                var payloadRequest = URLRequest(url: payloadURL)
+                payloadRequest.cachePolicy = .reloadIgnoringLocalCacheData
+                payloadRequest.timeoutInterval = 30
+                let (data, response) = try await URLSession.shared.data(for: payloadRequest)
                 guard let http = response as? HTTPURLResponse, http.statusCode == 200 else { return }
                 let remote = try JSONDecoder().decode(SyncGetResponse.self, from: data)
                 if let payload = remote.data {
@@ -221,15 +231,25 @@ final class SyncService: ObservableObject {
                 } else {
                     lastVersion = remote.version
                 }
-                lastError = nil
+                setError(nil)
             } catch {
                 syncLog("poll failed: \(error.localizedDescription)")
                 // Polling errors are transient; stay quiet unless nothing ever worked.
-                if lastSyncedAt == nil { lastError = "Cannot reach sync server" }
+                if lastSyncedAt == nil { setError("Cannot reach sync server") }
             }
         }
     }
 
+    /// `@Published` fires on every assignment, even when the value is
+    /// unchanged. The 5-second poll would otherwise republish `lastError`
+    /// forever, and since `PanelView` observes this object, the whole panel
+    /// (list, rows, overlays) re-rendered every 5 seconds — the app grew to
+    /// ~190 MB and ~90 ms of layout per poll over five days of uptime.
+    private func setError(_ message: String?) {
+        guard lastError != message else { return }
+        lastError = message
+    }
+
     private func restartPolling() {
         pollTimer?.invalidate()
         pollTimer = nil