The only files you should “Open” are LightBurn files. It sounds like you mean to “Import”, in which case it will show all supported file types, and point you to the last place you imported from.
“Import” means import new vectors into my current file, and this even works with LBRN project files - you can import the vector data from another LightBurn file into the current one, but it doesn’t bring the cut settings, just the vectors.
“Open” means replace the current project with the one on disk, including any cut data, if present. If you “Open” a normal vector file, LightBurn switches to Import mode for that file as a convenience, so you can double-click to launch other file types.
So it does work either way, but it behaves a little better if you use “Import” for artwork and “Open” for projects.