They do have the information - getting it to populate on a quote/invoice/job would be the way to go. I am not a computer guy so it sounds super simple to me. It could require a total re write of the way jobber works - I have no idea.
A workaround I did was use a zapier trigger. Anytime a job was changed I would have a message populate in Teams that said Job # was changed for the following reason "x". I also did it when a quote was approved, invoice status changed, and I forget the last zap. It was helpful to keep office staff up to date on what was happening in the field.
This has consistently been one of my biggest gripes using Jobber. Jobber does do several things well. This is an area of improvement in my opinion.