I had to reinstall my server files to keep the newest version of Rust and Oxide happy, but now, even with my necessary files put back in from my backup, it creates a new map file and wipes the old one. How do I play on the old version of my map with all my player's entities?

remember that there was an update with rust and sometimes the old stuff is not compatible with new stuff that FacePunch added to game so your old map will crash . so in short in serten instances its not posible . you can use the same map but player stuff might not work anymore

Check youtuber srtbull and one of his videos about wipeless rust and saving progress after the force wipe. Not sure why a lot of people look for this unless it's Minigames server and you do not wanna build all spawns again, otherwise it's becoming boring for everyone but in theory you can save everything and make it working after the forced wipe. Keep in mind because facepunch updates the game with new stuff and etc sometimes save can be scuffed and weird after the update.