Two different situations.
Dak was a rookie new to the offense, Romo was injury prone with Dak drafted to be groomed to replace him, everybody ahead of Dak got injured or beat out to be starter after Romo's injury, Dak showed starting potential in preseason games, and Dak went on an 11 game winning streak winning an NFC East Division title and homefield throughout the playoffs.
Cooper Rush is a veteran that has been with another team, was an UDFA, is very familiar with the offense, has won as a fill in but did not win a starters job against Andy Dalton who moved on making the opportunity for Cooper Rush to return to the Cowboys as a backup, and Cooper Rush has a bus driver game plan.
The only things in common is that 2016 and 2022 Dallas has good defense, both had bus driver game plans, they do not turn the ball over, and the head coach is a puppet for Jerry Dumbo GM Jones.