[integration tests] Automate low-effort tests from the manual test plan

[csweichel]

At the moment we do a lot of manual testing based on our test plan. With the advent of Gitpod's integration tests, we should strive to automate a good part of that test plan.

Part of this task is to decide which tests to automate. Criteria to consider are:

• implementation effort vs manual test effort: if it's easy to test manually, but hard to put into code (e.g. an end-to-end test using playwright), we're probably better of testing manually
• expected brittleness: if a test would depend on many external "fixtures" it might not be a good candidate
• common case: if the test tests a popular use-case, we should consider automating it to make us find out quicker if it breaks

Prerequisite: #2617 is merged

[geropl]

There is some progress made on:

• [#2658] Basic integration tests #3260
• https://github.com/gitpod-com/gitpod/pull/5177

Which stabilizes the tests and added some workspace tests, but also showed the current limits:

• gp is not usable atm: [gp] Support gp env by talking to server directly #3162
• user namespaces in workspace container: Make "kubectl exec" work for usernamespaced workspaces #3380

As both issues are scheduled for this cycle we're going to pause efforts here until those are resolved.