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/PanelView.swift

@@ -5,7 +5,6 @@ import UniformTypeIdentifiers
 struct PanelView: View {
     @ObservedObject var store: Store
     @ObservedObject private var sync = SyncService.shared
-
     @State private var composer = ""
     @State private var composerFocused = false
     @State private var composerHeight: CGFloat = ComposerView.oneLineHeight
@@ -84,8 +83,7 @@ struct PanelView: View {
             Spacer()
 
             Button { withAnimation(.easeInOut(duration: 0.15)) { showSync.toggle() } } label: {
-                Image(systemName: "arrow.triangle.2.circlepath")
-                    .foregroundStyle(sync.code == nil ? Color.secondary : Color.accentColor)
+                SyncDot()
             }
             .buttonStyle(.plain).help("Sync")
             Button { toggleSearch() } label: { Image(systemName: "magnifyingglass") }
@@ -881,3 +879,15 @@ struct PanelView: View {
         return (try? AttributedString(markdown: string, options: options)) ?? AttributedString(string)
     }
 }
+
+/// Sync status lives in its own view so a `SyncService` publish cannot
+/// invalidate the panel's list. Watching it from `PanelView`'s body meant every
+/// sync event — including the 5-second poll — re-rendered every row.
+private struct SyncDot: View {
+    @ObservedObject private var sync = SyncService.shared
+
+    var body: some View {
+        Image(systemName: "arrow.triangle.2.circlepath")
+            .foregroundStyle(sync.code == nil ? Color.secondary : Color.accentColor)
+    }
+}