My fiancé and I have lived together for 6 years with my 12 year old daughter and our 3 year old son. He works full time as a teacher. I work full time from home and put in just as much time/effort as I did when I was in the office (before covid.) I'm also finishing up my last semester in college.
I do all of the cooking and most of the cleaning, which I do not mind.
We recently developed a rotation system with the dishes. I would do them one day, my daughter the next day and my fiancé the following day. My daughter and I would always do the dishes on our designated "dish day." When it would get to my fiancé, it would pile up for days and he would ask my daughter for help.