Is the TP4056 for lithium polymer or lithium ion batteries?
The correct name of the 'LiPo' battery, is 'lithium-ion polymer' battery. dropping the 'ion' part makes some confusions but it's still a Li-ion battery. so yes. you can use that chip for charging LiPo batteries.

A lithium polymer battery, or more correctly lithium-ion polymer
battery (abbreviated as LiPo, LIP, Li-poly, lithium-poly and others),
is a rechargeable battery of lithium-ion technology using a polymer
electrolyte instead of a liquid electrolyte.

from Wikipedia.