[DO NOT MERGE - wait 8.16 release][8.16](backport #5878) [Flaky Test] Fix TestHTTPSProxy

[mergify]

needs #5928 to be merged first

What does this PR do?

It moves the close of the proxy and target http server to t.Cleanup()

Why is it important?

Just using defer was causing the last request log to be logged after the test had ended, what lead to a panic.

Checklist

• My code follows the style guidelines of this project
• [ ] I have commented my code, particularly in hard-to-understand areas
• [ ] I have made corresponding changes to the documentation
• [ ] I have made corresponding change to the default configuration files
• [ ] I have added tests that prove my fix is effective or that my feature works
• [ ] I have added an entry in ./changelog/fragments using the changelog tool
• [ ] I have added an integration test or an E2E test

Disruptive User Impact

• N/A

How to test this PR locally

On a Mac (the panics happened on Mac)

go test -count 10000 -timeout 0 -run TestHTTPSProxy ./testing/proxytest/

It should succeed

Related issues

• Closes [Flaky Test]: TestHTTPSProxy – data race #5869

Questions to ask yourself

• How are we going to support this in production?
• How are we going to measure its adoption?
• How are we going to debug this?
• What are the metrics I should take care of?
• ...

---

This is an automatic backport of pull request #5878 done by [Mergify](https://mergify.com).

[mergify]

Cherry-pick of 02fb75e has failed:

On branch mergify/bp/8.16/pr-5878
Your branch is up to date with 'origin/8.16'.

You are currently cherry-picking commit 02fb75e59e.
  (fix conflicts and run "git cherry-pick --continue")
  (use "git cherry-pick --skip" to skip this patch)
  (use "git cherry-pick --abort" to cancel the cherry-pick operation)

Unmerged paths:
  (use "git add <file>..." to mark resolution)
	both modified:   testing/proxytest/proxytest_test.go

no changes added to commit (use "git add" and/or "git commit -a")

To fix up this pull request, you can check it out locally. See documentation: https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/checking-out-pull-requests-locally

[elasticmachine]

Pinging @elastic/elastic-agent-data-plane (Team:Elastic-Agent-Data-Plane)

[elastic-sonarqube]

Quality Gate passed

Issues
0 New issues
0 Fixed issues
0 Accepted issues

Measures
0 Security Hotspots
No data about Coverage
0.0% Duplication on New Code

See analysis details on SonarQube

[mergify]

This pull request has not been merged yet. Could you please review and merge it @AndersonQ? 🙏