Torn between breaking up or giving another chance

We have been together 4 months, Me 37f him 41m. It started with him saying a wife and kids were a must for him. So that’s the mindset I went into thinking this guy was gonna get serious quickly.

But it turned out differently.

1 - he lives with his sister who is a single mom of a child that he is stuck babysitting every afternoon. I have confirmed this as true.

2 - he lacks ambition. I would think if someone wanted their own family they would fight tooth and nail to get out of this situation somehow especially since this is what he straight up told me at the start. He keeps saying his sister will graduate from college in 2 years and they will separate after that, but I just don’t get the sense of hustle/planning from either.

3 - he claims that someone stole his identity and got a $45k credit card in his name and he is struggling with credit. I dunno, but to me this sounds fishy. He says he has a job making $45k a year, but he drives a beat up car and wears the same clothes. Which wouldn’t be a problem except that he is stingy with me and has slowly started to be more entitled about my stuff/money. For example, he thinks of nothing to get into the backseat of my car which has become our makeout place and it’s starting to infuriate me. At first it was fun to make out there but I have told him it’s getting old and not to expect it anymore.

4 - we have never had sex despite all this making out. I feel confused. He will respond when I start kissing him and he gets it up but he never follows through.

5 - he never initiates dates. Im always having to come up with ideas and booking reservations, so I end up paying more on dates than he. This is also spilling over into us not having sex. I don’t know if we haven’t had sex because he doesn’t know how to book a hotel room or isn’t attracted.

So last week I decided to test him because my communication is falling in deaf ears and being ignored. We ended the date by agreeing that we needed to have sex and me telling him specifically which hotel to book so there is no ambiguity.

3 days after that day crickets. No mention of anything from him. Then I got sick and had to go to the doctor. He was texting me every morning after that asking how I was but never called.

It was also my birthday. He didn’t call to wish me happy birthday and only after I texted him the picture of my dads gift did he send me a delayed text message about how he will give me a gift.

No happy bday text or call though. He calls me the day after the bday and I was already over my infection and birthday. He didn’t bring up either, no belated happy bday, just everyday talk.

And now 3 days after my bday still no text/call.

I have been putting off buying a house in hopes that he would have a serious talk with me but it never comes and I am tired of always being the one to initiate “talks”.

We come from a minority immigrant culture which is why I’m torn.

I know he’d be a great dad since he cares for that child, but that’s all that’s left. I wish he would open up but he just shuts off my communication and lets his pride take over.

Should I dump him knowing Im unlikely to find a man from the same culture statistically and just go out there and accept to be self-sufficient? Or try again?