> LLM-s are not learning on the fly, but I suspect they do log the conversations, their responses and could also deduce from further interaction if a particular response was satisfactory to the user.

Seems like this is hard to reliably do across the board. Sometimes when I stop interacting it's because it nailed the solution, and sometimes it's because it went so poorly that I opted to bin it and do it myself. Maybe all of the mid conversation planning and feedback is enough though.