Same user cannot load another tab of Sourcegraph if the first tab has lots of pending GraphQL calls

Created by: limitedmage

• Sourcegraph version: 3.41
• Platform information: N/A

Issue reported by https://github.com/sourcegraph/accounts/issues/8205

Steps to reproduce:

1. Create a search that will have lots of pending GraphQL calls (for example, due to #40686)
2. While the search results load, open a new tab in the same browser and go to Sourcegraph

Expected behavior:

New tab loads Sourcegraph

Actual behavior:

Sourcegraph doesn't load, network tab shows that GraphQL calls are pending to load the page and won't complete until those in the first tab completes.

Opening a new tab in incognito mode does work.

/cc @sourcegraph/search-core