Dual screen problems

Hi, I have just bought a new 27” iMac and am trying to dual screen with my ‘late 2015’ 21.3” iMac. I bought a thunderbolt cable and thunderbolt 3 to 2 adapter. But after connecting the two, clicking ‘command’ And F2, nothing happened. I’ve swapped the ports around, reversed the cable, but it doesn’t show anything to indicate a connection. I phone Apple and after going through the setup. I was first told Big Sur doesn’t support this, which I can’t believe. I was then told my 21.3” Mac is too ‘new’. Again I find this odd. I am returning the cable and adapter to Apple. But would, before I buy another set of cables (I’ve a feeling that one or both could be faulty). Could some confirm whether these two macs can or can’t dual screen please. Thanks