Can you upload your design interview test/assignments in your portfolio?

If you've used code/assets they've povided you, most likely not as they are the company's property by default (unless amongst then there is a license somewhere that states you can share, like MIT for code, or CC-BY for artwork).

You can however remove any such assets, replace then with your own, and as long as it has no trace of the provided content (nothing, not one line of code or a pixel, in the files, caches, or git history whatsoever) then it's your work and you can do whatever you want with it.

If they provided you nothing apart from instructions and you did everything from scratch then again, it's yours.

Unless you signed a commercial contract or NDA they can't claim ownership on that even if it was something they requested you to do.