Several students in my class using Mac and Windows are unable to create a new game using Quest web editor because the site reports the error “Sorry, an error occurred while processing your request".

They can use the offline editor or upload a game zip file and then edit in the browser as a workaround.

Has anyone run into this issue?

Yes. There are quite a number of posts about it.

You can only create a game in secure mode. If the site address starts with http://, change it to https://. You might want to update your bookmarks as well.

In general, you should use https whenever you have the choice. It prevents other people on your network (or your ISP) from collecting information such as your username, password, and private messages. I think there are very few sites now that don't support it (and even fewer countries where there are legal restrictions on using it).