[SG-31709] Migrate integration tests from `mocha` to `jest`

Created by: gitstart-sourcegraph

Description

This Pull Request is about migrating the integration tests from mocha to jest within client/web/src/integration and client/browser/src/integration directories

SG Issue Gitstart Ticket

Test plan

• Run ENTERPRISE=1 yarn test-integration

Migrated Directories

• client/web/src/integration
• client/browser/src/integration