Looking at the output on the page, it looks like your template is loading Bootstrap 5 files. SCLogin on Joomla 3 expects Joomla's native (and old) Bootstrap 2 files to be loaded on the page.
Before we revert to an even older version of SCLogin, I'd prefer you try to make an edit to see if that works for you. Please edit the /modules/mod_sclogin/helper.php file. Around line 100, you should see:
if(JVERSION >= 4.0 || $jfbcBsVersion == '2')
Change that to:
That will force SCLogin to load Bootstrap 5 classes in our template file, which should make the popup work properly.
Please let us know how that goes. If it still does not work, please leave enabled so we can check other items. We'd much rather get SCLogin working as-is if possible.
Thanks,
Alex