Thanks for trying to improve I18N in GlotPress itself! But when making such large changes it's better to discuss them first so feedback can be provided earlier.

These are two separate issues which again should be handled in separate pull requests. For the JavaScript part it makes more sense to refactor this by using the wp-i18n JavaScript package and its wp.i18n API.

For the validation part, I'm not sure why you added the $message parameter to the second position. This seems like an unnecessary back-compat break.
Building the message like this is also still cumbersome and not easy to translate since the sentence is split into multiple parts.
I think it would be much easier if the full message, one for positive and one for negative can be provided and only the type and field names are (optionally) injected.

I think it's okay to use wp.i18n.{methodName} everywhere instead of having an extra variable.

To test this functionality, I have created the .pot file to add the new strings to the translation:

wp i18n make-pot . languages/glotpress.pot

This command adds the new strings:

Then I have imported this file in my local GlotPress and I have translated some strings like "Dismiss":

Then I have created the .mo file (glotpress-gl_ES.mo as I am testing with Galician language) and I have moved it to the wp-content/language/plugins, overwriting the current file.

I have reloaded the page content, to load the new translations, and then I have tried to translate a string with empty content, to fire an error, and the "Dismiss" text is not translated.

The updates in the JavaScript file are loaded fine, but the translation in the JavaScript file is not showed.

I have updated the file version for the common.js file, using the filemtime function, to look for some cache problem, but the result is the same.

wp_register_script( 'gp-common', $url . '/common' . $suffix, array( 'jquery', 'wp-i18n' ), filemtime(plugin_dir_path( __FILE__ ) . '/../assets/js/common.js') );

Am I missing some steps to test this code?