Using Client.Repositories.ListBranches does not get the branch's "protection_url" field (the Branch struct doesnt even have that field).
As can be seen in the documentation, the List Branches call returns a protection_url field:
https://docs.github.com/en/rest/branches/branches?apiVersion=2022-11-28#list-branches
Also just calling the endpoint demonstrates that.

I already created a simple fix and am about to open the PR.