Huh! I’m surprised that you are having that tight of a fit if you are using Proofgrade material, but there is something about the shape of the cut that might help with future assembly.
In profile, a laser beam doesn’t cut straight down, it cuts at a very slight angle. So the base of the shape (the part that was on the bottom when it was cut) is always going to be a little bit larger than the top of the shape. If the fit is a little tight, you can try turning the pieces over or flip them, they might fit better.
That’s just in general, but another thing that is very easy to do is just brush an emory board over the edges a couple of times. That’s usually enough to let it slide right in. Shouldn’t ever try to force fit it though, that usually results in a broken tab.
You can likely save the print though - use a little wood glue and clamp or tape the tab back on until it dries. Then a few swipes with an emory board and you can probably still use that one. It will be indistinguishable from new and stronger than a fresh print.