If you lose the templates styling when opening the modal via the iframe mode, see:
docs3.regularlabs.com/modals/faqs

Not sure. Maybe something weird with the URL routing on your site.
Can you give me (super) admin and (s)ftp access so I can take a look?
You can use the 'Confidential information' button in the forum editor to hide sensitive information.

In what module do you have these {modal} tags?
And can you also provide the (s)FTP credentials?

When I visit the website now:

Your site for some reason temporarily blocked me. You might want to look into that....

Anyway, Modals asks the Joomla core article router to create a non-SEF URL for the article.
That returns:That URL works.

It then passes that through the Joomla core router to create a SEF URL, which results in:That URL doesn't work for whatever reason.

I have no idea what is causing Joomla to render a non-working SEF URL. But this is outside the control of Modals.
So either some bug in Joomla or something not quite right in your setup.

See if you can get it to work by simply using the URL attribute instead of the article attribute.

We're talking about Modals here, not Snippets.instead of

Yeah, when articles have their own (hidden) menu items, it is a lot more stable. I guess Joomla gets confused with the active category in some weird cases.