Is there a way to put two linked cards directly next to each other without adding a space between them? When I remove the space, the cards seem to break or display incorrectly, as shown in the image below. How can I fix this?

With space

Without space

I never ran into this issue until I read your post. Yea it seems there's a bug. There must be at least one character (like a space) between cards for them to show up correctly.

Try putting a zero-width space character between them. It's an invisible character that does not have any width. You can copy it from this page and paste it in between your cards. You won't see anything in editing mode but it solves your issue.