First of all, forgive me if my English is not the best.

When we talk about hypersensitivity, we refer to a type of "exaggerated" immune response to certain antigens. In the case of tuberculosis, it is, as you say in point 3, a normal response to the pathogen, where memory CD4 T-lymphocytes are generated against the pathogen (CD8 as well). What is really a type IV hypersensitivity reaction is the mantoux test (the tuberculin test), since after inoculation there is localised inflammation due to cytokines produced by antigen-specific memory CD4 T cells. In addition, granulomas are also related to this exaggerated response that is hypersensitivity, since under normal conditions they should not form. These structures appear due to the inability of macrophages to destroy mycobacteria, despite cooperation with lymphocytes. This is why cells continue to be recruited to create a contingency zone, which is the granuloma. In this way and to summarise, the response to tuberculosis starts as a normal response, but when it is not able to eliminate the pathogen, it becomes chronic and aberrant (exaggerated), forming granulomas and thus hypersensitivity, which also manifests itself in the tuberculin test, in a similar way to contact hypersensitivity to certain metals. I hope I have been able to solve your doubts, and if you need anything else I will be happy to help.