I think that if someone has an issue with the car changing ends during a panic stop the cause is going to be either, overcorrection by the driver, brake or suspension problem front or rear, serious alignment issue, etc.
JMHO, but tread depth has nothing to do with sliding but the tire compound could have something to do with it.
Try putting a pair of new/very good tires on the rear of your vehicle, a pair of well worn ones on the front
The only problem there is using well worn tyres anywhere on the car!
this only checks the rear wheels. both front and back need to be checked for a hanging caliper.
Being a front wheel drive , it sounds as though both front wheels are not pulling equally as if it’s a problem in the differential. Maybe ? Reminiscent of the rear axle opperation with no positrak, just one side is driving. Does it always fishtail in the exact same direction ?