I lift weights and use TR, here is what works for me.
I currently lift weights / perform plyometric exercises 3x a week. I go to an olympic style gym and my lifting coach trains track racers. He understands I am into crits and short TT’s, so my volume isn’t as intense, but it’s still heavy.
I perform my lifts on the same day as my TR interval days, so that is T, R, and Sat. I do my TR workouts on my lunch break (WFH) and lift in the evening after work. This gives me Wednesday to do an active recovery day and Sunday to do low stress but a long ride. Monday and Fridays are completely off. I use the low volume plan, and insert rides of my choosing for Wednesday and Sunday (outside preferably). This works out to be about 85-100 miles / week. So think of it this way: 3 hard days, 2 easy riding days, 2 days completely off, per week.
I have no problem completing my workouts and I feel very strong on the bike, with no pain. Since most of my work is leg, glute, core focused, you would stand to believe it would be too much, but having real recovery days / rest days is absolutely how you do this. Diet plays a big role and I suggest you keep a food journal as well. More so during the build phase, where after ride nutrition is really important.
Upper body workouts shouldn’t be crushing your performance on the bike unless your diet is way out of whack.