JetBrains search box changes
Created by: vdavid
Follow-up PR for https://github.com/sourcegraph/sourcegraph/pull/35326 because I missed making the modifications @philipp-spiess pointed out at first.
Test plan
I've tested the functionality, and it works, so just test the code I guess. The only thing that's changed in the functionality is that the authenticated user is loaded from Sourcegraph before the app loads, so even the first search uses the user's token. Everything else is the same.
App preview:
Check out the client app preview documentation to learn more.