Ask whose computer this is, and believe the answer

Sign-out never cleared local storage. It stopped push, flushed settings and
removed the subscription -- that last one reasoned explicitly that a browser
left holding someone's mail becomes somebody else's next -- and then left the
settings cache and the recently-addressed list on disk. That list is other
people's addresses, and nothing ever removed it.

Clearing it on sign-out is now unconditional, because lending a laptop is the
same exposure as a public machine, only quieter. The keep-list is short and
deliberate: lastUser, which only a trusted device writes; the trust flag; and
the random push device id. Everything else goes, so a key added later is
forgotten by default rather than by nobody having thought about it.

"Keep me signed in on this device" defaulted to true, which assumed the answer
most costly to get wrong -- someone on a library machine got a thirty-day
cookie unless they noticed a ticked box. It now asks whose computer this is,
defaults to not yours, and says what each answer does. Untrusted means a
session cookie, nothing written locally, no push subscription, and a five
minute idle sign-out.

The idle timer is there because the alternative does not work: custom
beforeunload text was removed from browsers years ago, and no event fires at
all for walking away from a signed-in screen, which is the case that matters.
A timer needs nobody's cooperation.

Reads are gated as well as writes, since a machine trusted once still has the
residue; an untrusted sign-in purges it outright. The wire keeps calling this
`remember` -- it is persisted in SESSION_FILE, and renaming it would invalidate
every session file on upgrade for a change of vocabulary.

Verified in a browser against the mock, not only in tests: untrusted sign-in
leaves localStorage empty through a full session including folder expansion;
trusted writes settings, recent and lastUser as before; sign-out clears recent
and settings while keeping lastUser; an untrusted sign-in afterwards clears
even that.

web/src/lib/__tests__/theme.test.ts

@@ -1,6 +1,6 @@
 import { describe, expect, it } from "vitest";
 import { DEFAULT_SETTINGS, DEVICE_KEYS, acceptRemote, isDarkTheme, syncedPart, toggleTarget, useSettings, type Theme } from "@/store/settings";
-import { loadJson, saveJson } from "@/lib/storage";
+import { loadJson, saveJson, setDeviceTrusted } from "@/lib/storage";
 
 /**
  * "ihasmail" is a dark theme wearing ihasmail.org's palette. Everything that
@@ -60,9 +60,14 @@ describe("the default theme", () => {
         removeItem: (k: string) => void store.delete(k),
       },
     });
+    // Reads and writes are gated on device trust now, and the gate defaults to
+    // closed. These tests are about `loadJson`'s merge, so open it and put it
+    // back -- an untrusted device is covered by storage.test.ts instead.
+    setDeviceTrusted(true);
     try {
       fn();
     } finally {
+      setDeviceTrusted(false);
       Reflect.deleteProperty(globalThis, "localStorage");
     }
   };