[SG-39284] Upgrade yarn to the latest version

Created by: gitstart-sourcegraph

Description

Setup:

• Follow the official migration guide from yarn

Migrate:

• Remove yarn-deduplicate package, replace yarn deduplicate with native yarn dudupe
• Remove flags: —mutex —silient —ignore-script —ignore-engine
• Replace --cwd package/path with workspace package_name
• Append yarn in front of binary script in scripts config, ex. cross-env -> yarn cross-env
• Fix some TS build errors
• CI: Remove cache client/extension-api/node_modules
• CI: Add cache .yarn/cache

Refs

Sourcegraph Issue Gitstart Ticket

Test plan

Ensure that CI checks are green.

App preview:

• Web
• Storybook

Check out the client app preview documentation to learn more.