feat(auth): N3 — server-side multi-session account switch

Track every account that completes OAuth in a browser session (session 'account_ids',
~14-day cookie), so the user can switch between them without another Google round-trip.
New GET /api/me/accounts (switchable accounts, active flagged) and POST /api/me/switch
(guarded: target must be in the session list — proof it signed in here — and re-checked
against is_allowed in case the invite was revoked). Logout now signs out the active
account and falls back to the most recent remaining one, else clears the session. UI: the
account popover lists the other signed-in accounts (click to switch, reloads) plus an
'Add another account' action (-> /auth/login, which uses prompt=select_account).
Trilingual. Third step of Epic N.

backend/app/auth.py

@@ -16,6 +16,9 @@ from app.security import encrypt
 
 _EMAIL_RE = re.compile(r"^[^@\s]+@[^@\s]+\.[^@\s]+$")
 
+# How many recently-used accounts to keep switchable in one browser session.
+MAX_SESSION_ACCOUNTS = 6
+
 # Base sign-in requests only the non-sensitive OpenID scopes (profile/email). These do
 # NOT trigger Google's "unverified app" warning and do NOT expire after 7 days, so a new
 # user gets a clean, familiar consent. YouTube access is granted later, one step at a
@@ -175,6 +178,12 @@ async def callback(
     db.add(tok)
     db.commit()
 
+    # Multi-session: remember every account that has authenticated in this browser so the
+    # user can switch between them without going through Google again. Only accounts that
+    # actually completed OAuth here land in this list (it's the proof they may be switched to).
+    accounts = [a for a in (request.session.get("account_ids") or []) if a != user.id]
+    accounts.append(user.id)
+    request.session["account_ids"] = accounts[-MAX_SESSION_ACCOUNTS:]
     request.session["user_id"] = user.id
     log.info("Login: %s (id=%s, role=%s)", email, user.id, user.role)
     return RedirectResponse(url="/")
@@ -182,8 +191,16 @@ async def callback(
 
 @router.post("/logout")
 async def logout(request: Request):
+    """Sign out the active account. If other accounts have authenticated in this browser,
+    switch to the most recent one instead of fully logging out."""
+    active = request.session.get("user_id")
+    remaining = [a for a in (request.session.get("account_ids") or []) if a != active]
+    if remaining:
+        request.session["account_ids"] = remaining
+        request.session["user_id"] = remaining[-1]
+        return JSONResponse({"ok": True, "switched": True})
     request.session.clear()
-    return JSONResponse({"ok": True})
+    return JSONResponse({"ok": True, "switched": False})
 
 
 @router.post("/request-access")