Cannot use shared GitLab.com runners with `gitlab-org` tag for Docker in Docker

What does this MR do and why?

This customer emergency happened because a user with a Docker in Docker CI configuration decided to use GitLab-hosted runners, and saw the gitlab-org runner tag at the top of the list of shared runners. They decided to use it, and couldn't figure out why the Docker daemon was failing to start, until we realized they weren't using one of the saas-linux tags that actually supports DinD. Runners with the gitlab-org tag don't run in privileged mode, and cannot be used for DinD.

• #spt_self-managed slack thread: https://gitlab.slack.com/archives/C4Y5DRKLK/p1722881130394429
• #g_runner Slack thread: https://gitlab.slack.com/archives/CBQ76ND6W/p1722890287005259

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