Working for a bank i know there many aspects that come with being a PSP. Think about fraud detection, KYC, technical as well as well as financial audits. When you work with card processing you need to abide with Mastercard policies for example(which is a few hundred page rulebook). Same goes for various other payment methods with each their own rules, fraud rate tresholds. Then there are security aspects, risk apetite, chargeback policies as well as possible liquidity requirements.
My 2 cents is that this is a bit much for a side project. But I don’t know how much time and resources you have on your hands. As there is a reason people usually use larger payment providers and smaller payment providers usually attract a certain type of customers(p*rn, gambling, “research” drugs etc)
If you want to do this solely for your own company, perhaps the way to go is to tie a few existing psp API’s together. But in Europe since the wirecard scandal regulators have become more strict on PSP’s.
Hope this info helps you a bit and doesn’t encourage you, if you are really set on this you’ll find a way. But handling other people their money and payment infrastructure comes with great responsibility.