I recently found out that there is a new chat bug where if you join an Xbox party you lose ESO chat.
Furthermore, doing a hard reset and manipulating the audio settings did not fix either. I believe ESO chat or Xbox chat is “seeing” you in party chat and is kicking you out of ESO chat.
Not sure if this will permanently fix issue but this did bring ESO chat back for me. Update: Temporary Fix
Fix action I used: turn Cortana setting off if it is on or on if it is off, I believe this refreshes the audio forcing you “out of party chat mode” which I believe is happening.
This will do another reset to Xbox but your chat should return. This is the fix action I used for this “new chat bug” issue with party chat use. Good luck
Go to Xbox Settings->System->Cortana settings
Xbox will reset and you will be good to go until you do another party chat lol temp fix
Mr. was my Father's name, just the tips is fine.