ci: Use the browser_performance job template

Rémy Coutablerequested to merge
396357-investigate-review-performance-job-failure-follow-up-from-retry-review-apps-jobs-in-all-cases into master

What does this MR do and why?

The job now passes: https://gitlab.com/gitlab-org/gitlab/-/jobs/3971956061.

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

Related to #396357 (closed)

Edited by Rémy Coutable

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