In all of our experiences in Europe for accommodations this one was by far the worst.
First - the accommodations are up on the 4th floor. There is no elevator so get ready to climb with your luggage.
Second - the AC did not work at all. It never got below 86 degrees F in the room. We understand a little warm given the Italy weather in the summer but this was unbearable. Thank goodness we were only there for 1 night.
Third - the only “ancient palace “ feel to this place is the door and key that is given (one of 3 keys that you need to lug around and they’re not small). There’s nothing really that indicated palace or even an explanation of the history - although almost everything is antiquated and uncomfortable.
Fourth - Our bathroom was absolutely disgusting and clearly had some massive plumbing issues. Taking a shower the water took over 6 minutes to heat up and by the time it did the sound was so awful we were afraid that the pipes would burst. There was nasty caulking with mildew all over it.
Fifth - the room is SUPER SMALL. It does not have a bistro table with chairs as pictured. It has an old desk with a chair that could seat a 6 year old (maybe).
Overall if you are coming to beautiful Florence there are so many places to stay. I would keep looking if I were you.