Fix session replica behaviour (merge with session)

The harder-to-refactor parts are the places where exists/username/token
are called within a React component. However, `resetAndRedirect` and
`store` are already called from async contexts, so adding an `await`
is simple.

This thus merges the logic, keeping localStorage for the components to
call, but making sure reset/store behaviour works correctly for the
replica.

web/src/components/Login.jsx

@@ -24,7 +24,7 @@ const Login = () => {
     try {
       const token = await accountApi.login(user);
       console.log(`[Login] User auth for user ${user.username} successful, token is ${token}`);
-      session.store(user.username, token);
+      await session.store(user.username, token);
       window.location.href = routes.app;
     } catch (e) {
       console.log(`[Login] User auth for user ${user.username} failed`, e);