Can’t. Sorry. As the code in the projects widget queries projects post type entries. And it applies for the categories as well. The selected category slugs only display of which assigned for projects. To understand this better, try creating two categories (for testing purpose). Name category one as “Post Cat” and the second one “Project Cat”. You can create them from Dashboard > Posts > Categories > Add New Category.
Then create some posts (Dashboard > Posts > Add New); in Categories box, check “Post Cat”.
Then create some project (Dashboard > Projects > Add New Project); then in the Categories box, check “Project Cat”.
Compose a new page from Dashboard > Pages > Add New. Insert a Projects widget, then try to put the category slug of “Post Cat”. Normally it will read post-cat. Publish page and visit the page. See the result.
Second, edit page, then change its slug to “Project Cat”, that normally read project-cat. Update and see the result.
At this phase, I hope I’ve explained myself well.