There is lots of information you tell the chat that should be considered by the training plan. Now it is: when you mention a preference, the chat offers to save it, for example:
Cool! Just to be sure, if I mention today I don’t like to run Mondays, it will ask to save it to the prompt as your example. After plan regeneration, will that line in the prompt disappear?
That line will stay unless you change it either directly or via chat. Basically you can think about your plan system prompt as a ‘you edited section’ + ‘chat edited section now’