This is likely related to my recent changes supporting long queries, where the "Execute" button now does a form post referring to the query by its saved ID on the server, rather than having the query text in the body. The servlet is apparently not presenting the correct credential to retrieve the query from storage.
One workaround is to click the "bookmark" icon instead, which encodes the query in the URL path query. Another workaround, especially for longer queries with no bookmark icon, is to copy the query text from the "saved queries" page.
Fixing this is given a lower priority due to the existence of the workarounds, and that configurations using HTTP authentication on the Sesame server with multiple users are probably still uncommon.
Tomcat, with openrdf-server configured