Just one possible solutions is to create a custom post type for projects that has an archive. On the project post you have a user field relating the project to a user, or users. A user field stores an array of user IDs in the DB. I would then use something like this to put the values of the user field into a standard WP meta field in the DB https://acfextras.com/dont-query-repeaters/. Then I would add a pre_get_posts filter that runs when the archive page is loading to filter project posts by the currently logged in user.
