CI: Push docker test-kit after tests

[donhardman]

Bug Description:

We currently push the docker test-kit image before running the CLT tests. However, if the tests fail, we might end up with a corrupted build that gets used in other repositories like manticoresearch-buddy and so on. To prevent this issue, we should move the docker test-kit push to a later stage after all tests have successfully completed without any issues.

Manticore Search Version:

Latest dev version

Operating System Version:

Ubuntu Jammy

Have you tried the latest development version?

• Yes

Internal Checklist:

^{To be completed by the assignee. Check off tasks that have been completed or are not applicable.}

• Task estimated
• Specification created, reviewed, and approved
• Implementation completed
• Tests developed
• Documentation updated
• Documentation proofread
• Changelog updated

[sanikolaev]

Done in #2194

Tested in https://github.com/manticoresoftware/manticoresearch/actions/runs/9126437962/job/25095466084#step:5:25