Reported as “login screen isn’t always immediately visible.” The actual
bug was upstream of LoginPage entirely. Every real route, including “/”,
sits behind ProtectedRoute (App.tsx), and ProtectedRoute returned null
while AuthContext’s api.me() call was still pending on first load.

Most visits land on “/”, not “/login” directly, so the sequence was:
render nothing -> wait for /api/me -> get 401 -> Navigate to /login ->
LoginPage finally renders. The blank stretch is proportional to how long
/api/me takes (cold backend, slow network), which is why it only showed
up “sometimes” - a fast response made the gap invisible.

Fixed ProtectedRoute.tsx to render the same “Loading…” text used by
AcceptInvitePage instead of null while loading is true.

Not touched: LoginPage.module.css’s 0.4s fadeIn on .loginCard. That’s a
deliberate entrance animation, not a bug - once the blank-screen race
above is closed, it just reads as a normal fade-in.