Simplify the triggerring of 'gitlab-docs' Review App pipelines

What does this MR do?

This makes the project compatible with the new version of the script made at gitlab!53361 (merged).

Why was this MR needed?

Because the docs Review App deployment was made simpler in gitlab-docs with gitlab-docs!1493 (merged), but this requires a few changes to work with gitlab!53361 (merged).

Example Review App (fetching the trigger-build script from the simplify-docs-review-app-trigger branch): http://master-runner-2809.178.62.207.141.nip.io/runner/

What's the best way to test this MR?

What are the relevant issue numbers?

Related to gitlab-docs!1493 (merged), gitlab!53361 (merged), and omnibus-gitlab!5085 (merged).