I want to respect your ability to make descisions for yourself. But my advice:

1. Open your mind to doing exercises that achieve the same goals with different equipment. Eg, you can increase effective pull up weight by switching to assisted one arms, then one arms, rather than stacking on increasingly huge numbers of plates. There is no such thing as the magical, perfect exercise - they all work about as well, unless you are competing in Mr Olympia. Pick the one that is most convenient for you and the equipment you have.
   1.1) I would also say - I don’t want to doubt your commitment nor your current fitness level. But I notice you said you plan to do insane shit on this pull up bar. A far faster and cheaper solution could be a $10 used doorframe pull up bar that you use until you outgrow it. A solution doesnt have to be perfect forever for it to be perfect right now.
2. Scope out the municipal gyms near you, and look into financial aid programs. A gym with a simple barbell or dumbbell set, plus a pull up bar, is really all you need. Or if it is full of machines, that is great, too. Don’t let the perfect be the enemy of the good.
   2.1) I will note that while I can imagine you putting togther a free standing pull up bar for next to no money using salvaged materials, I think you will find that achieving sufficient stability, durability, and load bearing capacity will be a bit of a feat of engineering. If you are trying to do, like, weighted kipping pull ups or muscle ups or something, the dynamic, non-vertical forces could quickly make your joints unstable via the large torsional forces you would be putting on the base. Making a truly resiliant free standing pull up bar is going to be much easier for someone who buys their materials new, uses good tools (like miter saws and hole saws, which are expensive), and who has a decent amount of carpentry experience under their belt - and doing it this way, even if you manage to borrow the most expensive tools, you can still expect materials to cost a couple hundred bucks with the price of lumber these days. A municipal gym membership, otoh, is probably like $15/mo.
   2.2) Same with buying dumbbells. Expect iron to cost between $1-2/lb. While building a functional home gym is a noble goal, a cheap commercial gym is often a better value.
   2.3) One more point on the gym and then I’ll shut up, which is that I, personally, like gyms because they help me stay consistent with my training by putting it somewhere other than my home - so if I can motivate to go to the gym, I will get my workout in. Versus at home, I tend to be far more likely to procrastinate, since the option is always available. Plus, good gyms often have a social aspect that can be enjoyable.
3. You should find a different place to live asap. These kinds of landlords are, like, literal slumlords. Their whole ploy is to rent to someone they think has no other options so they will never complain or move out, then nickle and dime them as much as they possibly can. I would start reading up on landlord-tenant law, start documenting issues that you see, and get in contact with a lawyer (many will do free consultations to give you advice on your situation). If you have proof of issues of habitation, you can pay a lawyer, like, $50 to write a letter on their letterhead to your landlords saying you’ll sue them if they don’t let you break your lease and give you your full deposit back.
   3.1) Seriously, you’re getting scammed. I know you are grateful to have any roof over your head, but that is exactly how people like this will exploit you. If you put the legwork in, you can find a place that is as cheap or nearly as cheap without shitbag landlords - and a landlord that charges more up front but doesnt nickle and dime you will probably leave you ahead financially.
   3.2) If you won’t do it for your pocketbook or quality of life, do it for your gainz. Inhaling mold spores results in systemic inflammation, which decreases sleep quality and recovery.