I’m not really that knowledgeable about AM5 mobos (still on AM4) but you should be able to get something perfectly sensible for 100 bucks. Are you going to get as much IO and bells and whistles no but most people don’t need that stuff and you don’t have to spend a lot of money to get a good VRM or traces to the DIMM slots.
Then, possibly bad news: Intel Gen 13 supports DDR4, so you might need new RAM.