feat(app): show the connection in use on host switcher rows

The old marker only ever tagged the local host as "Local" based on its
server id. Each row now shows the connection actually in use, inline
after the host name — the TCP or relay endpoint (default :443/:80
stripped), or "Local" for socket/pipe transports.

packages/app/src/screens/settings-screen.tsx

@@ -895,8 +895,9 @@ interface HostPickerProps {
 /**
  * Scopes the four host sections to a host. Reuses the canonical sidebar host
  * switcher pattern (left-sidebar.tsx): a quiet row-styled trigger opening a
- * <Combobox>. The local host is listed first and tagged "Local"; an "Add host"
- * row is always reachable from the list — even with a single host.
+ * <Combobox>. The local host is listed first, each row shows the connection it
+ * is using right now; an "Add host" row is always reachable from the list —
+ * even with a single host.
  */
 function HostPicker({ activeServerId, sortedHosts, onSelectHost, onAddHost }: HostPickerProps) {
   const { t } = useTranslation();
@@ -906,7 +907,6 @@ function HostPicker({ activeServerId, sortedHosts, onSelectHost, onAddHost }: Ho
     sortedHosts.find((host) => host.serverId === activeServerId) ?? sortedHosts[0] ?? null;
 
   const handleOpen = useCallback(() => setIsOpen(true), []);
-  const hostLocalMarkerTestID = useCallback(() => "settings-host-local-marker", []);
   const hostOptionTestID = useCallback(
     (serverId: string) => `settings-host-picker-item-${serverId}`,
     [],
@@ -929,12 +929,11 @@ function HostPicker({ activeServerId, sortedHosts, onSelectHost, onAddHost }: Ho
       anchorRef={triggerRef}
       includeAddHost
       onAddHost={onAddHost}
-      showLocalMarker
+      showActiveConnection
       searchable={false}
       title={t("settings.hostPicker.switchHost")}
       desktopMinWidth={240}
       addHostTestID="settings-add-host"
-      hostLocalMarkerTestID={hostLocalMarkerTestID}
       hostOptionTestID={hostOptionTestID}
     >
       <ComboboxTrigger