Similar issues here. Some “custom html” widgets working normally, but others containing a shortcode won’t work (the public page shows the shortcode as text).
The same shortcode works if it’s inside a “text editor widget” (but the “custom html” widget is needed to correctly manage a couple of manually set <p> paragraphs, that the editor widget would ignore and erase).
In this case, migrating to the new and fancy blocks system is not an option, it’s a large and old website that just worked fine.