Will a 2016 Mazda BT-50 tub liner fit the 2022 model?

Almost certainly not. The 2016 Mazda BT-50 was a shared model with Ford (Ranger) but in late 2020, the BT-50 was replaced by an all-new model which was a platform sharing deal with Isuzu (D-Max).

Even if the dual-cab tubs of each version of the BT-50 were dimensionally similar, there would be dozens of detail differences (tie-down points, tailgate width, hinge placement, wheel-arch intrusion etc) that would mean the tub liner from one would not fit into the other. The good news is there are plenty of tub-liners available for the new BT-50. Most seem to be priced from about $300 to $500. And since the previous model BT-50 was a popular vehicle, you could probably sell the old tub liner you have to offset the cost of the new one.