Stall recovery is absolutely required to be instructed and demonstrated in the private pilot checkride. These are demonstrated to a full aerodynamic stall, not merely to stall warning.

Spin recovery is no longer required to be instructed (and was not previously required to be demonstrated during the practical test either [as many aircraft are placarded as "intentional spins prohibited"]).

CFR for the instruction requirements: https://www.ecfr.gov/current/title-14/chapter-I/subchapter-D...

Airman Certification (Practical Test) Standards: https://www.faa.gov/training_testing/testing/acs/private_air...