So many unknowns, if you could hook up tune ecu and see that coolant temp and how the fan is reacting would be good. Have you checked the coolant temp plug for corrosion, could be coolant temp sensor giving bad reading, need to see temp to make sure. Have you checked fuse 7, fan relay fuse, check across probes not just visual, make sure that relay you bought is compatible as i have swapped relays with a no go then had another handed to me and bingo. It’s probably, relay, coolant temp sensor, or coolant sensor plug, fuse number 7 fan relay fuse, fan plug, pinched wire, a few possible items to check off