Hey Dan,
in principle, the portfolio page template displays all projects there are, and the tag archive pages display only the projects with a specific tag. There are two ways to proceed here – either use tag archive pages in both cases, so that projects are always separated according to their tags, or customize the WP_Query object in the “page_portfolio.php” template to exclude projects with a certain tag. If you choose the second path, I might be able to help you in constructing the custom query.
Sincerely,
Andrii / Satori Studio