@Pascual, Emmanuel Thanks for reaching here! If understood right when deploying to web app with private endpoint from azure devops you are facing 403 error. Because the endpoint is private for the SCM too, the DevOps Agent must be in a network with access with the endpoint, so its mandatory to use Self hosted Devops Agent.
Have you configured custom domain?
Refer to this official document- https://learn.microsoft.com/en-us/azure/app-service/networking/private-endpoint
Suggest you to refer this similar discussion here might be helpful.
Let us know.