Is UART a Mealy machine?
The term "Mealy machine" (or "Moore Machine" or whatever other terms you have at your disposal) is rather a way of looking at systems or way a system can be implemented. 

I.e. asking whether some generic system (here: UART) is this or that machine doesn't make sense. It can be seen and implemented as Mealy machine but it can also be seen or implemented as Moore machine or as Turing machine or as register machine or as stack machine or...

One way may be more or less appropriate but many are possible.

So if you ask whether something is a Mealy machine that something must be a way of how a system is described or implemented (the diagrams you are referring to); but we don't know what diagrams you are talking about.