TCX is a Garmin format that was supported by Edge units even back in 2004. The TC refers to (Garmin) Training Centre as it’s the native database format for that software. It has elements built into the schema that the GPX schema has no equivalent for. TCX has supported turn by turn prompts from it beginnings more than 18 years ago, as that’s what Garmin courses (CRS) support, and CRS is a subset of TCX. Adding the turn prompts back then wasn’t as automated as now though!
For compatible turn (or other type) prompts with Garmin Edge units, TCX is likely your best choice.