I have a normal (no pro) PS4, which has no 4K function.
My Netflix account has a 4K function and my monitor too.
Can I watch movies I stream on Netflix on PS4 in 4K, or is not it?
No it's not possible. If the device you're looking for does not support 4K, you can't.
I think it is transmitted over the Internet
Not, unfortunately
Nope, your PS4 can only spend a maximum of 1080p.
The normal PS4 supports the output of 4k content. However, the content is limited to pictures and videos and not to games.
Netflix would have to support 4k.
Source and setting for 4k output: https://www.giga.de/...instellen/