Migrate integration tests from `mocha` to `jest`

[umpox]

Part of https://github.com/sourcegraph/sourcegraph/issues/31707

Implementation

1. Migrate all tests in client/web/src/integration from Mocha to Jest
2. Migrate all tests in client/browser/src/integration from Mocha to Jest
3. Ensure tests still run and pass as expected

Notes:

• Due to previous issues, this PR did the opposite migration: https://github.com/sourcegraph/sourcegraph/pull/7872. It could be helpful to look at that PR for an idea of what changes might need to be made.
• Jest has a codemod that could help with this. See these docs: https://jestjs.io/docs/migration-guide#jest-codemods. I tried this briefly but it didn't seem too effective. Use with caution!

[gitstart-app[bot]]

Here is the GitStart Ticket for this issue: https://app.gitstart.com/clients/sourcegraph/tickets/SG-31709

[umpox]

~@gitstart-sourcegraph Please don't start work on this yet, I'll confirm there's no major objections to this in a meeting tomorrow~

Free to work on!