You mean you actually expected to find an answer in Microsoft documentation? I'm sorry, I know that is sarcastic. It really is terribly frustrating how incomplete Microsoft documentation is, and the fact that they don't seem to care much about improving it.
I'm pursuing the same question. Theoretically, there must be some performance hit for double encryption. That said, from the scant information Microsoft has documented, the second encryption is occurring at a hardware level and should present very little performance impact.
I did find this bright spot for MySQL infrastructure double encryption (https://video2.skills-academy.com/en-us/azure/mysql/concepts-infrastructure-double-encryption), which states that a 5-10% performance impact can be expected. That is a big impact -- more that I would expect from hardware level encryption. So maybe I'm reading something into the documentation that is not there, or maybe this figure is only applicable to MySQL. In any case, it does create cause for concern on how double encryption would impact our non-database workloads.
I've just about come to the conclusion I need to set up a lab and do some benchmark testing since Microsoft is not helping us out much. I'm posting this in hopes that somebody has already done this, and can provide results. Or maybe Microsoft can step up with some tangible information about the impact (or non-impact) of double-encryption?