All PCs are a frankenstein mix of parts, that's the beauty of PCs. Components can be mixed and matched and usually work together well.
So instead of a new PC think of how you can evolve your current PC. You may be able to upgrade the CPU or even better replace the motherboard and CPU but keep the case and other components for now until you can afford to make more changes. If that's too expensive then look at upgrading other components until you can do a big shift with the motherboard and CPU. For example get an SSD if you don't have one, maybe uograde the graphics card for a gaming boost etc.
Don't think of a PC as being a single thing - any component can be upgraded and switched out at any time and you can gradually move to your dream PC over time in steps, which spreads the cost over time. It's easier to find a few hundred pounds / dollars / euros every 3-6 months than it is to find £2k in one go, and you can still end up in the same place if you're patient
The most important base components are definitely the motherboard and CPU though (it determines the ceiling of all the other components) - so make sure any changes you make fit with your long term plans for those. For example if your PC is old then start with the motherboard and CPU so you aren't restricted in other components (E.g. RAM options are better on newer motherboards so it's worth waiting to buy RAM if you intend to do a big motherboard upgrade).
E.g. If I were starting from a basic ATX desktop, I'd aim to get a new motherboard first and ideally a good CPU. But I might get a decent motherboard with a modern socket and a cheaper CPU if I was short on cash. Then later when I have money again I'd sell the cheaper CPU and upgrade it to something better that my new motherboard can support. I might keep my current hard drive and then when I can afford it get an m.2 to make better use of the new motherboard. RAM can be brought from the old board, and even upgraded in steps to get to an eventual goal amount. Like start with 8gb or 16gb but eventually move to 32gb or 64gb when I can afford it. I might keep my current graphics card and then upgrade that once the other components are good. I might even buy a second hand older card so I get a boost until I can afford my dream card so I at least move forward of I had a crap one now. It'd take time but I'd be moving forwards every few months getting a better and better PC without having to find a huge amount of money in one go.
Think of it like the ship.of theseus. Genuinely my current PC has evolved gradually since 2015 but I don't think I have a single component left from that original PC apart from maybe some screws and the case. I've done 1 big motherboard change and 2 CPU changes since then, I'm onto my 3rd GPU and about to move to my 4th, and have replaced the RAM and then doubled it later with 2 more sticks. I've changed the power supply once, and lost count of how many hard drives I've been though - currently I have 2 m.2 cards and some SSDs of various ages.