Tricky.
It depends what he wants and what he is willing and is doing.
And also what you want.
Its fair enough you're frustrated. But equally taking out that frustration on him vs talking about it and exploring it and wanting to understand his angle is v different. There is no such right or wrong.
As partners you should both be advocating for the others happiness. If buying a house is important to you that should be something he is supportive of, but equally you should be supportive he has a job? You are both in your own right to make decisions about your own lives. But it's important for a relationship to talk about them, and have consideration for the impact and understand how the other person will receive it.
And then keep evaluating if the relationship is right for you.
Effectively is he planning and taking action to get a better paid job. Is that important to him. Is he happy to stay put. How long for. Are you happy to accept that or do you want a more financially rich aprtner. Is he willing to step up to meet your needs or not. Then you can decide from there.
It is probably not easy for him to magically get any job. It's unfair to judge him on his success when it's not his decision if he gets picked for a job. But it is fair to hold him accountable for his effort, especially if he has said and promised he is going for a salary that is more than what he's on.
Really you just need to talk. To understand what his angle is, where he's at. And what his plan is. What he cares about investing in you and how his career choice effects your relationship. And then evaluate if it's going to be a place where your happy or if it doesn't meet your needs.
Its not fair to harbour resentment for someone without raising your concerns. And it's not good to stay with someone and make them feel inadequate. If he isn't going to step up to what you need, you should consider leaving him. If he isn't able to step up, but wants to that's more tricky. Maybe you allow a time frame or try and rough it for a bit.
People say love should be there without money. But as an adult paying your own way or having open discussions about who's bringing what to the table and both being valued is important. Happiness relates to health.
Maybe you're at peace paying for yourself and him also. Maybe you're not and you want a partner with ambition and action.