I ran a local site on WordPress Studio (SQLite) and hit a fatal error during Toolset’s upgrade when it tried to ALTER TABLE wp_toolset_relationships to add the autodelete_intermediary column (duplicate column error), preventing access to the admin side.
Solution:
This environment isn’t supported by Toolset; the fix was to use a standard WordPress stack with MySQL/MariaDB (e.g., MAMP/WAMP/Local WP/XAMPP) or migrate to a regular host, after which the issue no longer occurred.