Ive watched every video on youtube. It is all for 2018 r3s and lower. Not one video for the new r3. What year is yoursCheck YouTube for a video from "Sportbike track gear"/STG. Brian Van does a really good video explaining how to do it. You will need to loosen the other end of the throttle cables from the throttle bodies to fit the R6 throttle tube. That is the only way to fit the R6 throttle tube. It's not difficult, just take your time. I have the same bike, and it's definitely worth the effort-
All years of the R3 use the exact same chassis. all that changed for 2019-2020 is the forks, and bodywork (mine is a 2019). That being said, it sounds like something got either pinched, or misrouted? Also, there is a "peg" on the inside of the switch on the throttle side, that goes into a hole on the handlebar (to keep it from rotating on the bar), make sure that is seated. Does the throttle turn smoothly when it's not mounted on the bike? It's a good idea to (lightly) grease the outside if the bar, and inside if the throttle tube as well. Good luck-Im able to get the cables onto the r6 throttle tube but when i try to put the cable assembly back in the switch handle it is super tight to align and once it is the throttle is stiff, and doesnt return all the way.