I have stopped using Office programs, mostly because I don't want to deal with setting up Wine. I am making a birthday card for someone, but I noticed that LibreOffice Draw doesn't have the Borders and Accents menu like Publisher does. Is there something that can replace it (website/extension/menu)? I'm looking for something like the blue and yellow block border (not very decorative).
Sorry if it's not a direct answer, but I can suggest you try inkscape instead. Of course it's a much more powerful program, and that comes with it being possibly a bit harder to grasp and definitely different from publisher, but it should be very easy for a beginner to make a simple birthday card collage.
I think inkscape is a better solution as well. Draw has some limitations. However you can use Inkscape to create this borders you want, and then load It in Draw, If you find yourself more familiar with Draw