The NFL introduced a new ‘hybrid’ kickoff style for the 2024 season. Receiving a lot of criticism early in the season, the reasons for the new rules are solid.
The reasons: increase returns and decrease injuries.
Here’s the breakdown
If the ball is kicked inside the landing zone (20yd line to goal line; red zone), the ball must be returned. If the ball is kicked past of the landing zone or out of bounds, the ball will be placed ay the 40 yard line. The ball may still be returned if it rolls to the end zone or kicked to the end zone through the air. If the ball is kicked into the landing zone, rolls into the end zone and gets downed by the kickoff team, it will placed at the 20-yard line. If the ball is kicked through the air to the end zone and gets downed, it will be placed at the 30-yard line.
Every member of the coverage team (kicking team) aside from the kicker has to have one foot on the 40-yard line. The coverage team cannot move until the ball is touched by the return team or hits the ground in the landing zone. The return team can have 9 or 10 players blocking in the set up zone depending on whether it has one or two returners (max two). The return team must have at least seven players on the 35-yard line (they can have two or three players off the line but in the set up zone). The return team cannot move until the ball is touched or hits the ground (referee will signal when they can move since their backs will be turned to the landing zone).

An onside kick is only legal in the 4th quarter and must be declared by the kicking team.
Full list of rules can be found here.
Information taken from NFL Operations and The New York Times.