Fix failed build-conan-pkg job

What does this MR do?

Fixes gitlab-org/gitlab#321550 (closed) and gitlab-org/gitlab#337626 (closed)

In this MR we're changing the Conan package manager to a project-specific one. With this, we don't need to follow the strict policy for package naming.

With this MR, we also add back skipped tests. They are fixed as well accordingly.

As this MR is tech debt, we don't need changelog entry

What are the relevant issue numbers?

Does this MR meet the acceptance criteria?

• Changelog entry added
• Documentation created/updated for GitLab EE, if necessary
• Documentation created/updated for this project, if necessary
• Documentation reviewed by technical writer or follow-up review issue created
• Tests added for this feature/bug
• Job definition updated, if necessary
  • Job definition example
  • CI Templates (to be removed)
  • Vendored CI Templates (also in CE)
  • Ensure that all of the ENV vars supported are propagated to Docker containers upon docker run in job definitions
• Conforms to the code review guidelines
• Security reports checked/validated by reviewer