I had grounds for a postponement, but I didn't have time to get it. I was detained on the street and taken to the TCC. Can I appeal such mobilization?

If the grounds for the postponement were present, but were not formalized procedurally (documents not submitted, procedure not completed), then legally the postponement does not exist. A person without a valid postponement is subject to mobilization. The mere fact of the existence of grounds without their formalization is not a basis for canceling mobilization.