Technam P92 student pilot reported on landing with crosswind loss of directional control resulted in a runway excursion.

Narrative

Day 0; at approximately XA:15 on my 3rd solo flight; first off airport solo; I was on approach at ZZZ for RWYXX. I was crabbed into the left crosswind component of approximately 6 knots and felt confident in my approach. Airspeed was steady at 55 knots; and flaps were set at 30 degrees. As I entered the roundout in ground effect; I noticed the aircraft was floating as I passed over the 1;000ft markers. In response; I reduced power and initiated the flare for touchdown. I added right rudder input to align the aircraft with the centerline; but upon touchdown; the aircraft moderately bounced. However; I did not feel unsafe and maintained backpressure to prevent porpoising. The aircraft bounced lightly two more times before the nosewheel made contact with the runway.Upon nosewheel touchdown; I retracted the flaps and began increasing power for the touch and go. As the aircraft accelerated; it started veering toward the left side of the runway. I applied full right rudder; but there was no noticeable change in direction. Recognizing the issue; I pulled power and lightly tapped the brakes. The aircraft continued to drift left and ultimately coasted into the grass at approximately 40 knots. While in the grass; I maintained control; pulsing the brakes until the aircraft came to a full stop. The propeller remained clear of any strike; and RPMs stayed constant.After coming to a stop; I promptly shut down the aircraft and notified ATC. They dispatched a ground crew to push the aircraft back onto the taxiway. I was then instructed to taxi the aircraft back to the ramp; with a chase vehicle following to check for any anomalies. No issues were observed during the taxi.