feat(desktop): show splash overlay during server switch

ServerKey's keyed <Show> remount is a multi-second synchronous cascade (dispose + rebuild of the whole app subtree) that used to leave the UI looking frozen. A tiny module-level serverSwitching signal now gates a fullscreen Splash rendered above the ServerKey boundary, and the status-popover click handler setTimeout-defers the batched navigate+setActive so the browser paints the splash before the freeze begins and dismisses it after the new subtree paints.

packages/app/src/app.tsx

@@ -28,6 +28,7 @@ import {
   Suspense,
 } from "solid-js"
 import { Dynamic } from "solid-js/web"
+import { serverSwitching } from "@/utils/server-switch"
 import { CommandProvider } from "@/context/command"
 import { CommentsProvider } from "@/context/comments"
 import { FileProvider } from "@/context/file"
@@ -305,6 +306,12 @@ export function AppInterface(props: {
   router?: Component<BaseRouterProps>
   disableHealthCheck?: boolean
 }) {
+  // ServerKey wraps the whole Router so that switching `server.key` throws
+  // away any session / pty state from the previous server. Preserving the
+  // route across servers doesn't work because session ids, pty ids, and
+  // most URL-addressable resources are server-scoped — you'd 404 on every
+  // fetch. The click handler that swaps servers also navigates back to "/"
+  // so the fresh MemoryRouter doesn't try to re-resolve a now-dead URL.
   return (
     <ServerProvider
       defaultServer={props.defaultServer}
@@ -312,6 +319,11 @@ export function AppInterface(props: {
       servers={props.servers}
     >
       <ConnectionGate disableHealthCheck={props.disableHealthCheck}>
+        <Show when={serverSwitching()}>
+          <div class="fixed inset-0 z-[2147483647] bg-background-base flex flex-col items-center justify-center pointer-events-auto">
+            <Splash class="w-16 h-20 opacity-50 animate-pulse" />
+          </div>
+        </Show>
         <ServerKey>
           <GlobalSDKProvider>
             <GlobalSyncProvider>

packages/app/src/components/status-popover-body.tsx

@@ -15,6 +15,7 @@ import { useSDK } from "@/context/sdk"
 import { normalizeServerUrl, ServerConnection, useServer } from "@/context/server"
 import { useSync } from "@/context/sync"
 import { useCheckServerHealth, type ServerHealth } from "@/utils/server-health"
+import { setServerSwitching } from "@/utils/server-switch"
 
 const pollMs = 10_000
 
@@ -292,13 +293,26 @@ export function StatusPopoverBody(props: { shown: Accessor<boolean> }) {
                       aria-disabled={blocked()}
                       onClick={() => {
                         if (blocked()) return
-                        // Run navigate + setActive in the same tick so Solid
-                        // disposes the old subtree once instead of cascading
-                        // the route change disposal into the ServerKey remount.
-                        batch(() => {
-                          navigate("/")
-                          server.setActive(key)
-                        })
+                        // Paint a full-window splash BEFORE the heavy
+                        // ServerKey remount so the user gets visual
+                        // feedback during the multi-second synchronous
+                        // dispose cascade (xterm + file-tree + providers).
+                        // setTimeout(0) yields to the browser so the
+                        // splash lands on screen before the cascade
+                        // starts; a second setTimeout(0) after the batch
+                        // waits for the new subtree to paint, then
+                        // dismisses the splash.
+                        setServerSwitching(true)
+                        setTimeout(() => {
+                          try {
+                            batch(() => {
+                              navigate("/")
+                              server.setActive(key)
+                            })
+                          } finally {
+                            setTimeout(() => setServerSwitching(false), 0)
+                          }
+                        }, 0)
                       }}
                     >
                       <ServerHealthIndicator health={health[key]} />

packages/app/src/utils/server-switch.tsx

@@ -0,0 +1,9 @@
+import { createSignal } from "solid-js"
+
+// Global flag used to paint a full-window splash overlay while a server
+// swap is in progress. ServerKey's keyed <Show> remount is a big
+// synchronous cascade (dispose + remount of the entire app subtree) that
+// can freeze the UI for several seconds; setting this true before the
+// swap and false after lets us render an overlay above the ServerKey
+// boundary so the freeze has visual feedback instead of looking stuck.
+export const [serverSwitching, setServerSwitching] = createSignal(false)