I think Fitzgerald is smart enough to understand what happened to Shero/Hynes. If Shero had the balls to dump Hynes after 2019, he may have gotten another year or two. He certainly made plenty of other mistakes and would have gotten fired eventually, but Shero was too stubborn and didn't fire Hynes until it was far too late. He tied an anchor around his own neck and ended up paying the price.
I think it's also pretty clear they're not enamored with Ruff, despite what many posters on here want to believe. If they liked him as much as you think they like him, they wouldn't have taken until October to re-sign him after his contract expired. They wouldn't have put an out-clause into both his original deal and his new extension. Lindy was never going to be the long term answer and we all knew that the second he was hired, he was brought in to teach the kids and establish culture. We are beyond that now.
Fitz has often talked about how he doesn't like making in-season roster moves because of his experience as a player - when he himself got traded, it took him a while to get any traction with his new team. I think he feels the same way about coaching, which is a MUCH bigger disruption because the whole team deals with it, not just one guy. So I doubt we see an in-season coaching change unless he gets a mandate from ownership (and it sounds like they're pretty hands-off at the moment, but that might change with some more embarrassing home losses).
If they miss the playoffs, Lindy is toast. I genuinely believe they were days away from firing him in October 2022, that 15 game winning streak saved his job. They ran it back with basically the same roster and nearly every player has regressed. Ultimately the head coach is responsible for the teams performance.