I see this as a very important aspect of playing in general (including a live gig), but I wasn’t able to tell how this was defined in the thread. I would say “just be yourself,” which is something that anyone should be able to pull off. Having gig’d with a truly authentic leader, I have to say that it needs to be first and foremost. From an audience perspective, if there isn’t a mix of originals and creative covers, I may as well stay home. I can spin up a playlist from original artists on spotty in a heartbeat.
Also, there is a lot to parse here, which brings me to thinking that a more concise/smaller bulleted list would probably be more useful.
EDIT: Oh and make sure you have a tuner handy. LOL