Panes do not correctly reflect Login status

If I am logged into a React SDK app (e.g., https://generator.inrupt.com), and then open my Profile in the same browser, I can edit any of the Profile fields (so I am clearly logged in and authorised), but below the Profile I see "Log in" and "Sign UP for Solid" buttons which seems to infer that the Data Browser does not think I am logged in.

To Replicate

1. Open https://generator.inrupt.com
2. Log in via the Login screen.
3. Display the Profile.
4. Edit a Profile field just to confirm I am logged in and authorised to edit the Profile.
5. Click the WebID link shown at the top of the Profile page.
6. A new browser tab opens, and the Data Browser Profile for the logged in user is displayed.
7. Edit a Profile field just to confirm I am logged in and authorised to edit the Profile.
8. Scroll down to the bottom of the Data Browser Profile page.

Expected Behaviour

1. "Log out" button displayed, illustrating I am logged in.

Actual Behaviour

1. "Log in" and "Sign Up for Solid" buttons are displayed.

Dev Notes

• If I click the "Log in" button, the standard Log in dialog is displayed. Selecting the appropriate log in method, a "Logged In!" message is displayed, but I am not prompted to enter a password.

Reproduce the issue from https://generator.inrupt.com by logging in, opening the Profile, and following its WebID link to the Data Browser Profile. Inspect the Profile page's login controls and verify the fix by confirming that an authenticated user sees a "Log out" button instead of "Log in" and "Sign Up for Solid."