Migration assistant source not working

I recently got a new iMac and I’m in the process of transferring data from my old iMac to the new one. I have the migration assistant up on both computers and the receiving iMac has found my old one and says “checking Monica’s iMac” with a spinning wheel while my old iMac just says “discoverable as ‘Monica’s iMac’...” with the spinning wheel. Both are next to each other and connected via WiFi. My old iMac was just updated to the latest software. My concern is that my old iMac isn’t able to find my new one, because my understanding is that my old iMac should have produced a numeric code that would match the one on the new iMac, but I haven’t received such a code.