A pre-solo private pilot student is training in a Cessna 182 they purchased, do they also need a high performance endorsement, as well as the solo endorsement prior to their first solo flight?
Yes. In order to solo, a student pilot must act as pilot-in-command of that aircraft, which requires a logbook endorsement for high-performance airplanes in order to do so per §61.31(f).
Additional training required for operating high-performance airplanes.
(1) Except as provided in paragraph (f)(2) of this section, no person may act as pilot in command of a high-performance airplane (an airplane with an engine of more than 200 horsepower), unless the person has -
(i) Received and logged ground and flight training from an authorized instructor in a high-performance airplane, or in a full flight simulator or flight training device that is representative of a high-performance airplane, and has been found proficient in the operation and systems of the airplane; and
(ii) Received a one-time endorsement in the pilot's logbook from an authorized instructor who certifies the person is proficient to operate a high-performance airplane.