Hi - I think I have discovered a bug.
When using type="module", we end up with 2 type attribute declartions, which is syntactically incorrect as far as I know.
The 2x type declarations did not seem to cause any issues until we recently updated WordPres to 6.4.3, and now the script tag is resolved in the browser to only have the type="text/javascript" attribute - module is removed, so the JS will not load.
The fix would be to ensure that the type="text/javascript" is removed/replaced when type="module" is inserted.