the reason your Posek doesn’t allow a Kli Shlishi that he is chosesh to the Aruch haShulchan that upholds that the process of tea even in a Kil Shlishi is considered “gmar’ bishul or Bishul Kal
It’s also a Mishnah Berurah.
Whereas, instant coffee is already “cooked” processed.
We’re talking about non instant coffee.
Also, being that even if you leave tea in cold water it will process, so its not the “cooking”…
Now, i’m not sure about ground coffee, as coffee if left in a “cold brew” for many hours it will brew as well..
Both tea and coffee will “brew” if soaked long enough.