What is the relationship between spiritual path, sectarian affiliation, and ascetic mode?
Cannot be described perfectly as you request as these are not exactly defined terms.
The easiest is sectarian affiliation, which simply means which sect do you identify with or belong to.
Spiritual path is a vague term, not used or defined in scripture. It can mean mean many things. Sometimes the religion you follow, or sect you belong to, or yoga methods you do, or philosophical school, or a combination, or other things as well.
Tapasya are the spiritual practices that you do to purify your mind to help you realize God. Again in general it is those things you do to control your mind and senses. It can mean many things in practice and what may be tapasya for you may not be tapasya for another person.. Practicing meditation is tapasya. Practicing silence is also. Fasting is tapasya. Japam is tapasya. The same general tapasyas are practiced across different sects and different religions.