Game engines, especially purpose built ones for in house use, are very modular, or can be modded to whatever their needs are. The engine has nothing really to do with it... for the most part. The networking would be the same regardless of what engine they used, that's something that's always modified by a bigger studio, they wouldn't use the built in UE5 for instance.
Dice wants to make everything look nice and high quality over performance. It's always a balancing act, and in some regards BF6 performs really well. However, there's too many animations, too much geometry, too many variables with spread, basically, there's way too many things that shift around people's hit boxes in game. When you have weird collisions with objects, that's going to affect the servers ability to predict and accurately track players. You can see people bounce off of stairs, animations, and lots of very strange jittering. These are game design choices, and a big part of the problem. You can either have smooth tight game play, or overly detailed geometry with 100's of animations which causes sloppy interactions. You have to pick one because you can't have both.