What is the proper term for "contraction economics?"
It doesn't look like there's an established term. Combine "demographic decline", "population decline" or even "fertility decline" (although this doesn't imply population decline) with whatever you are interested in (markets, economic growth etc.)

These papers (if macro) usually get JEL-tagged "J11 Demographic Trends, Macroeconomic Effects, and Forecasts" in combination with whatever is getting modeled, e.g. "Scotland the Grey: A Linked Demographic–Computable General Equilibrium (CGE) Analysis of the Impact of Population Ageing and Decline" is tagged with J11 and a bunch of R1x codes, the latter for regional economics/models.