Sounds like you’re in a constant state of stress. We as men have incredible burdens that rarely gets talked about, and we aren’t good at sharing our burdens with others. I imagine this is basically your schedule
Wake up decently early to get ready and go to work, you come home from a long day at work (and maybe a long commute) and immediately start supporting your wife in her career and helping around the house. Then the kids get to bed around 8:00 if your lucky and then you start cleaning up the house and you finish around 9:30-10:00. After this you get to choose to either have some alone time or go to bed to get enough sleep.
You don’t get much time to yourself to decompress and are exhausted, and like you said you don’t complain to your wife because you feel like she has enough on her plate. I also suspect that when your wife has something that comes up that she would like to do like go have girls night you are 100% supportive of her going out and having a good time while you stay home and get the kids to bed. But you likely never ask your wife if you can do something because you feel guilty putting more on her plate.
You’re not alone. I’m right there with you as everything I just said is from my personal experience.