Wallet connecting and authorization in different dapps

So i am having a little misunderstanding.
My question is, when i am connecting to dapp pops up wallet extenison

and when i inspect that pop up in url i see this
so this part is static(chrome-extension://dldjpboieedgcmpkchcjcbijingjcgok/popup.html?s=)
but string after changes all time.
I am trying to connect wallet to bridge while using playwright.
From where that data comes so i will be able to recreate url?

This is something that the team might have a better idea of. Meanwhile you can checkout this code here. Is this what you are looking for?