What does the language switcher next to my avatar do?

It's the flag icon next to your avatar, top right. Clicking it only changes what language the ExactSDS website itself is displayed in — menus, buttons, and labels.

It has no effect on any SDS document — your SDS keeps whatever content and language you configured for it in Section 1. If you're looking to change the language an SDS's own content is written in, that's a separate, required field in Product Details.