Respawn developers had to work towards preventing DDOS attacks on the game. This led to the cross-progression feature to get delayed. With the year coming to an end and no official update on the feature just yet, players are likely to receive the update in 2022.

There are other answers below:

Cross Progression coming to Apex Legends on late may, 2022. Even if the cross-progression plugin does not bring 100% cross-play features to the game, it will be a very useful arrangement for many players.

Respawn Entertainment game director Chad Grenier addressed the challenge of adding cross-progression when Apex Legends hit Nintendo Switch in March.

Apex Legends Cross-progression: Is It In-Game? Sadly, Apex Legends cross-progression still hasn’t arrived as we ticked on over into 2022, but we had expected as much. As part of a Reddit AMA, Director of Communications Ryan K. Rigney suggested the difficulty of making cross-progression a reality.

Respawn has stated that cross progression will be coming to Apex Legends in 2022.

Cross-Progression for Apex Legends in 2022. While you will have to wait for 2022, it’s exciting to see Apex Legends integrate cross-progression for its users.

Seems like cross-progression support for Apex Legends is still a ways out at this point. Developer Respawn revealed that cross-progression is currently scheduled to go live in Apex Legends in 2022.

In a Reddit AMA in August 2021, though, Apex Legends’ former director of communications Ryan K. Rigney noted that cross-progression is coming “next year” (2022).

Apex Legends producer Josh Medina confirmed “next-gen console support” was in progress for 2022, as well as cross-progression.