> Does it say GPLv3 on the tin, or does it say "Compatible with GPLv3"?

As per [1], it says GPLv3 on the tin.

  > If you mix BSD and MIT code, the result doesn't suddenly become one or the other, but rather a combination of both, right?

The two pieces of code retain their original license, but you can distribute the combined work under just BSD.

[1] https://interoperable-europe.ec.europa.eu/collection/eupl/li...

yes and that is always true for code

but the situation for artifacts produced from the combinations of code under different licenses is messy in many ways (not just related to this cases)