ci: reenable prettier and enable ESLint for all workspaces

Created by: valerybugakov

Context

Re-enabling the prettier CI check disabled here. The original issue was found in the external contribution PR and was discussed in the Slack thread.

During the investigation of the prettier issue, I found out that we do not run the ESLint check for the VSCode package. This PR fixes that. Changes from this PR are tested on top of the external contribution changes in this draft PR.

Test plan

1. CI is green.
2. The prettier check is stable.
3. The VSCode package is linted with ESLint on CI.