This is s subject that has pissed every website coder off. There are so many examples on the internet showing how you can resize youtube videos to be responsive (work on all devices). Not all of them work and some invole custom css and wrapping your video in special code. (F*ck That)
If you can avoid writing css and use some king of plugin it is the easiest solution.
This Plugin works well resizing your wordpress videos from youtube. (Not framed just link)
Zendy Video Resizer
Over the years this has been a problem with some themes or css and the youtube videos don’t resize on a phone well. I have solved the problem various ways but often it pops up messing up my video display on mobile. This plugin didn’t have many reviews and wasn’t tested on the latest WordPress but it works well on mine.