You can use the GitLab API for listing protected branches.
GET /projects/:id/protected_branches
From there, you can use in your local repo git config
or git notes
to leave a "marker" to your branches.
Note that GitLab 15.10 (March 2023) includes a nice GUI for this:
See all branch-related settings together
All branch-related protections now display on a single page.
To see a unified list of your branches and all their protection methods, go to Settings > Repository > Branch rules
.
Each branch shows the merge request approvals, security approvals, protected branches, and status checks configured for it.

Previously, these settings were grouped by type, making it tough to see a holistic view of a specific branch’s protections.
We hope this change helps you discover, use, and monitor these settings more easily. We’d love your feedback in issue #388149.
See Documentation and Epic.
And this video