SO doesn't help much...

Hey guys, I'm looking for a little guidance on something. I've known my SO for about 7 years, we started dating almost a year ago and have been living together since November. He doesn't have kids but I do. I have a 2.5 year old. Anywho, I've recently explained to him that I'm feeling depressed and a little unmotivated to keep up the apartment. I've asked him if he could help around a little more than just the couple nights a week he starts laundry but doesn't finish them (I have to load the dryer and fold them and put them away.) A couple nights a week, he'll do the dishes but won't wipe counters down or sweep and mop or he'll just load the dish washer and tell me it's ready to start (I usually start them and put them away.) A couple times a week, he'll make the bed...so on and so forth with things that need to get done.

I've discussed with him that I think a honey to-do list is a little childish since he's 33 years old and knows what it takes to keep a household running. He kind of has the "old school" mentality of, "I bring home the bacon, you do the rest" kind of shit and it pisses me of to high heavens.

My daughter is home with me all day, tues and fri. My ex has her on weds and Thurs nights and stays the weekend with my ex until from Sat morning to Sunday night around 8 pm. So my current SO has her mon and Tues nights. I work sun night through Thurs night from 7 pm to 10 pm. I make really good morning so I can work part time with this job and still help with bills.

But like, how do I tell him this shit has to stop and he needs to help more often. There are more times than not, that I feel overwhelmed, thinking that I have to be the only one to maintain the apt? He hasn't cleaned the bathroom since he's moved in, he's mopped and swept a handful of times, helps me with my daughter but doesn't do much of anything else. I'm tired of feeling overwhelmed. I even tried an experiment where I kept saying what needed to be done, I did nothing and "waited" to see if he would start anything...and he hasn't.

A few weeks ago, he tried to tell me he was tired because he works two jobs and I pretty much jumped down his throat because of how much I have my daughter, very little time to myself and a whole shit ton of shit to do while home each day before work. I told him I don't want to spend my off days and weekend while my daughter is with her other parent to clean the apt...I shouldn't have to do a major clean session when it's MY time to relax or some self care....

So I guess the guidance I need is...how did you get your partner/ SO to help you more around the house? I don't want this to be a fight but I'm ready to boot his ass out the door 🤦‍♀️ he told me he could be lazy...but like, wtf dude, lazy doesn't even begin to describe the shit he doesn't do....HELP!?!