My husband and I do this. I use my iPad and he watches the tv (for streaming services). The easiest way for us to sync manually is if he plays his show and I press fast forward to be ahead of him by a few seconds, then I quickly pause and unpause repeatedly until I get it just right. Sometimes it takes a few tries, but you’ll get pretty good at it if you practice. It’s way easier than trying to hit unpause at the same time. I hope this helps a bit.

Unfortunately, digital rights management, can really get in the way of very ordinary and convenient ways of doing things. I can't think of a legal way of going about bypassing that restriction.

That said, I can think of a very crappy way of going about this, but it's .. yuck.. the idea pains me to suggest but maybe just maybe it's passable for now....

Point the ipad at the tv using the camera app.. you could even go as far as buy a separate webcam that you can plugin which just sits in a dedicated spot in the living room pointed just perfectly.

Another thought I had is that if your content is streamed through a box of some kind that has hdmi out to the tv you could get a hdmi splitter. one side goes to tv, other goes to a second screen like one of those portable monitors for digital nomads that work at cafes with their laptops. It may be necessary to get a splitter that strips hdcp from the signal I don't really remember so a bit of trial and error or further research required for that.

most people want the bigger screen and that's that.
Look for a watch party feature in your streaming apps.