fix: an open popup follows a network switch the background saves (closes #650)

When the background saves a network switch after the user approves a
site's request, or another popup page saves one, an open popup takes the
new network from the stored record inside a save, holding the lock, and
checks the record once at start-up for a switch saved before it
listened. It then leaves the page as a switch in Settings does: the cut
and the redraw are two Settings functions both paths call, and both
reset the popup's caches through one function. A switch in Settings is
now made inside its own save too, so one picked while a follow waits for
the lock is made after it. The popup never switches the network itself.

Model: opus-5-5

tests/e2e/firefox/run.js

@@ -867,6 +867,14 @@ step(
             "the page was not told of the approved switch: " +
                 JSON.stringify(events),
         );
+        // The popup, open all along, shows the new network
+        // (https://git.eeqj.de/sneak/AutistMask/issues/650).
+        await d.switchToWindow(env.popupWindow);
+        await d.waitFor(
+            "the open popup to show the testnet banner",
+            `const banner = document.getElementById("debug-banner");
+             return banner !== null && banner.textContent === "[TESTNET]";`,
+        );
 
         await openNetworkPrompt(env, "switch-restore", sepolia, mainnet);
         await d.click("#btn-approve-network");
@@ -881,6 +889,10 @@ step(
             isDeepStrictEqual(await storedNetwork(env), before),
             "switching back did not restore the mainnet network and endpoints",
         );
+        await d.waitFor(
+            "the open popup to drop the testnet banner",
+            `return document.getElementById("debug-banner") === null;`,
+        );
         await d.switchToWindow(env.dappWindow);
     },
 );