When would one use the word "participance" in place of "participation"?

The Oxford English Dictionary includes three words that all appear to have the same meaning: participation, participance, and participancy. I'm curious if there is a difference between the three.

participation n. The process or fact of sharing in an action, sentiment, etc.; (now esp.) active involvement in a matter or event, esp. one in which the outcome directly affects those taking part. Frequently with in.

parˈticipance n. rare = participancy n.

parˈticipancy n. the fact or quality of participating in something.

The word "participation" is far more common than the latter two. This answer lays out a distinction between participation and participancy, but I am still unclear if participance can be differentiated between participation.

What is the difference between the word "participation" and the word "participance"?

One difference is that since participance is used less commonly, it sounds a bit formal, and one expects to hear it in contexts such as politics, law, etc.

Another difference, in my view, is in the meanings of the suffixes "-tion" and "-ance (-ence)":

"-tion" is broader in sense, indicating state, condition, action, process, or result

while "-ence", having a more limited signification, only means "the act of ____" and is bare of any other possible connotations.

One such distinction can be seen here: https://wikidiff.com/continuance/continuation

On the meaning of "–ance" and "-ence": https://www.newtimes.co.rw/section/read/231328