Much like there is 64-bit "code", there is also 32-bit "code" that can only be executed in the 32-bit (protected) mode, namely all the BCD, segment-related, push/pop-all instructions that will trigger an invalid opcode exception (#UD) when executed under long mode. In that strictest sense, "64-bit and 32-bit code can’t be mixed".

Isn't it how recent Wine runs 32-bit programs?

This is also true on Windows. Malware loves it! https://encyclopedia.kaspersky.com/glossary/heavens-gate/