According to your own server configuration would be really useful to configure gitlab-ci-multi-runner shell executor to run as the user you need (to perform action within your permission contexts).
As I read gitlab-ci-multi-runner, if started as service, runs as gitlab-runner user.
I dug in forums and documentation and it seems it is not possible.
So this is more a “desiderata” request than a troubleshooting post.
Thanks!