Using async programming itself should not negative impact the performance. In fact, in many cases it increases performance, or necessary for user have a good experience (i.e. user thread isn't blocked, especially given Javascript by default is single threaded.)
The performance of callbacks vs promises vs async await are all about the same for most practical purposes. Since you are using them usually for network calls (or other forms of I/O), the I/O themselves are going to be the bottleneck compared to any sort of code inside the callback or promises mechanisms.