I experiance the same on both ipad and mac when using safari for youtube. on mac it seems to help for me to just open youtube again from favorites and search for the video again.
On ipad I have to completely close safari and open again going into youtube and write the name of the video again.
It is super annoying.
Over the years with safari on ipad and iphone.. Its been everything from annoying blue warning lines, videos that does not play, UI problems, pip problems, slow ui. 2 blue lines of warning, now it is a touch ui so bad you cant touch the screen without the video pause, you need to touch certain place to view timeline and with big chance you press the timeline... when i do need the “full screen“ pause it is not working with me.. I would say it works 50/50
I never touch the side menus on youtube with ipad... scrolling the have not worked for me in years.
It is a horrible experiance.. the idea is to push you to the app so you have to pay for you tube red to get rid of ads. but the app is horrible for a large ipad... i use desktop mode both for iphone and ipad.