Acc change in Bearby not reflected in Connect wallet pop up

Context
@peterjah you asked to test switching accounts on Bearby. Tested on the integration branch.

Flow from Connect wallet:

• When on the Connect wallet pop up
• Open Bearby and switch accounts in the extension.
• In the pop up, the address hash doesn't change. It keeps displaying the first connected wallet.
  It is not updated in the main Bridge window as well, after I close the pop up before reloading the page.
• Address hash is updated when the page is reloaded.

Flow from the main Bridge window:

• Connect account 1
• Close pop up, From the main Bridge screen, open Bearby and switch to account 2.
• Shown as connected is changed.
  This behavior should be everywhere. User shouldn't have to reload the page to see the correct account displayed.

How to

1. update account info without user having to reload the page (without user action).
2. The most minimal alternative would be to tell the user to reload the page or add a refresh icon, if 1. can't be done.

Technical details
Give the technical insights so anyone in the team can tackle the tasks - Dev

QA testing
Does this task require some QA tests ?
If yes, explain how to validate it

Start by reproducing the account-switching flows in the Connect wallet pop-up and the main Bridge window described in the issue. Trace how the selected account is refreshed after switching in Bearby, then verify that the displayed address updates without a page reload, or that the documented fallback is available.