[dev]: add e2e test for dev workflow (yarn watch)

[jsjoeio]

After hours of debugging and a false positive with a dependabot PR, we've come to the conclusion that we should have testing in place for our dev workflow: yarn watch.

This will prevent issues like #2962 from happening again.

One way to achieve this is by:

• adding a new script called yarn test:watch which is similar to yarn test:e2e
• add new CI step/job for running the e2e tests against code-server running with yarn watch

We'd have to add some timeout or sleep though since running with yarn watch takes time to finish.

Related:

• fix(dev-deps): limit ts-node upgrades #2962
• Breaking changes v9.0.0 -> v9.1.0? TypeStrong/ts-node#1283