Buck-Boost transformers are almost always installed as autotransformers. Does the National Electrical Code (NEC) permit the use of autotransformers?

Autotransformers are very common and recognized by all the safety and standard authorities.

You can refer to N.E.C. Article 450-4, “Autotransformers 600 Volts, Nominal, or Less”, as a reference publication. Item (a) details over-current protection for an autotransformer, and Item (b) covers an isolation transformer being field connected as an autotransformer for a Buck-Boost application.