Yes! Any google font chosen will automatically add it automatically.
You can also upload fonts in your organization settings which will generate it as well. Additionally, if you add @font-face css in your code, Builder will pick it up on any page it’s used in Builder and display it in the font dropdown menu in the Style tab.
From your first screenshot, it looks like you may have accidentally tried uploading a different file type (vnd.oasis.opendocument.formula-template) instead of a .otf file. Can you try uploading the Poppins-SemiBold.otf file again? If this doesn’t work, can you share the .otf file?