“Add Project Restriction” feature on org-level contexts is buggy. The popup is obviously creating paginated API requests to /project?organization-id=<my_org>&page-token=, but the implementation just keeps issuing requests without stopping. As a result, the dropdown to select project is not populating with any project names, hence rendering the UI unusable.
This feature is not available via API, as it says “NOTE: API support for project restricted contexts is coming soon” on doc.