Never had an issue watching sports through Youtube TV, Paramount +, Peacock or ESPN +.
I have never had a situation where part of the game was missed due to buffering issues - so that's new. Didn't happen to me though, I watched via CBS on Youtube TV.
Obviously if you start streaming any content - not just sports - on multiple devices, there is always going to be at least a second or two difference between each of them. There's absolutely nothing that can prevent that, no matter how fast your connection is or how low your lag is between the device, your router, possibly a cable modem and then your provider.
Personally I find the ability to watch when and were I want, with DVR controls, pausing when needed and the overall lower cost far outweighs tiny inconveniences like a few seconds delay. At least 1/2 the games I watch aren't live anyway - I'm not getting up at 5am on a Saturday to watch Liverpool. I'm going to watch that on demand in my own time. And I'm not going to try to watch European games mid-week during my lunch, I'll wait until I get home.
It is possible to not look at social media or sports websites for a few hours. You'd be surprised at how painless it is, plus bonus, you get to do something worthwhile with your time instead.