Thanks for the help. You can't imagine how useful your answer was to me. I would be picking at least 7 different workarounds if I didn't reach you.

Just to clarify and let the step-by-step guide:

1. Pick an option: User-assigned or System-assigned managed identity. I had picked System-assigned one.
2. To enable managed identity you need to go to "Identity" section in the left panel. You can simply enable system-assigned or create a user-assigned one and add it to the the list.
3. Go to your DevOps organization settings and add this identity as a new user to the whole organization (you might have to give it admin permissions).
4. Now you can select the managed identity in this HTTP request block as Authorization header.