Ok, found out what was going on. To diagnose such errors go to the semantic model and try to write a DAX query that will access all the tables, eg.:

In my case it turned out that my workspace was missing an identity:

Resolve the error to see results

{"error":{"code":"Premium_ASWL_Error","pbi.error":{"code":"Premium_ASWL_Error","parameters":{},"details":[{"code":"Premium_ASWL_Error_Details_Label","detail":{"type":1,"value":"We are unable to refresh the semantic model because the model uses a data connection configured for Workspace Identity authentication, but the workspace has no identity, or the model owner does not have permissions to use the workspace identity. Please configure a workspace identity and make sure the model owner has Contributor (or higher) access to the workspace, or use a different authentication method."}}],"exceptionCulprit":1}}}

Going to Workspace settings -> Workspace Identity -> Create a workspace identity fixed the issue (just to be sure query again, refresh the model, republish the repo, etc.).