Electromagnetism, relativity and Bernoulli’s law

I recently watched several videos about magnetism and relativity. It occurred to me that Bernoulli’s law might explain the relation between the movement of electricity and magnetism. Think more about it.

Here the links to the videos.

How Special Relativity Fixed Electromagnetism

https://youtu.be/Ii7rgIQawko?si=2TA0tvjOcUkm3mUd

How Einstein saved magnet theory

https://youtu.be/d29cETVUk-0?si=-eSpnan9CNpSJlqv

How Special Relativity Makes Magnets Work

https://youtu.be/1TKSfAkWWN0?si=_Eh6I6yzF_q9EPg8

I haven’t thought enough about the first video. The second and the third videos don’t seem to be right. Electric charges are moving. But the wire is not moving. I can’t see how electric density got higher if wire is not shorter.