My suggestion is to add a “pin” feature, enabling users to pin important convos to the top of the list.
(I know there in chronological order, but some convos get lost in the shuffle.) (I’m also aware of the ‘project’ feature.)
Another feature I think would be helpful is time and date stamps, like a text message conversation. This would allow users to refer back to a timeline of their projects for productivity tracking, etc.
Lastly,
It would be AMAZING if you could “restore last version” of the conversation.
I’ve seen variations of this on the desktop model when working on specific documents.
But recently, I accidentally pressed the 
refresh answer button at the top of a chat and it wiped the whole conversation post that question.
Some version of these features may be available via accessing the codes— user friendly & obvious versions would be extremely helpful for us, less-technicalogically-advanced folk 