keep all tabs open per default

There is currently no option to do that, but give me 30 minutes. I will check if i can find a way to do this easily.

Are you familiar and able to make a simple modification of your theme function.php file ?

Ok, this one is a little bit jank.
You can try to add this code to your function.php file.

add_action( 'wp_enqueue_scripts', function(){
    wp_add_inline_script(
        "mywpglossary-glossary",
        "jQuery(document).ready(function(){
            Query('.mywpglossary-list-entry-title').trigger( 'click' );
        });"
    );
});

What it does is add a little bit of javascript to click on each title to open them after the glossary script has loaded.

not the most elegant way to do this but it may work fine in your case.

Can you expose your use case ? This way we can see if we have an interest in implementing this functionality in a proper manner. But kwon this is a low priority for us, this may take some time.