Ok, it doesn't currently work because I cannot force push to Azure DevOps git repository on a change in Pagure git repo. From Azure side, there is hard-coded protection to /refs/pull/* namespace because the same references are used by the pull request functionality on Azure side.
I filed https://developercommunity.visualstudio.com/content/problem/1000581/please-allow-overriding-refspull-namespace-protect.html to see if that could be updated to allow repository admins to waive the protection.

Pushes to other namespaces happen just fine. It is also possible to send notifications of a remote Git repository changes, like Azure github app does. The only issue is that there is no way to trigger such operation in a native. One possibility is to create a Web Hook server side that would listen to Pagure or FedMsg and do operations on Azure side similar to how it is done with Github app. For this to happen, I still hadn't figured out how to create a build pipeline that would allow to specify remote yaml file (it is not supported for a remote git connection).

I triggered manual run for the master branch in Azure. You can see it here: https://dev.azure.com/bind-dyndb-ldap/bind-dyndb-ldap/_build/results?buildId=1&view=results