So... uh.... What is this? I was pasting my tile just fine, but this? I don't know how to describe it

What led to this, exactly? Without being able to reproduce this bug (if that’s what it is), it’s unlikely it can be fixed.

Not exactly sure

It looks like you enabled Random mode, which makes the Stamp Brush place a random tile from your brush instead of the entire brush. Click the dice icon in the toolbar to disable it. You probably hit the default keyboard shortcut d by mistake. You can change or unassign it in Edit > Preferences > Keyboard.

(Sorry, at first I thought this happened when placing the entire stamp, you didn’t explain/show that single tiles were getting placed, that would’ve clued me in sooner. Fortunately, you did the good thing and included the entire TIled window in your screenshot :D!)

I see now, thanks!