I am not sure I am understanding you.
You say the modal does not work. But when I look at your page, the modal pops up fine.
Yes, it is opened using the full screen width. But that is because you have not set a width. If you want the modal to open smaller to a specific size, use the width (and optionally height) attributes.
In the very beginning I have explained that I am migrating from joomla 3 to joomla 4. I now understand that the pop-up under joomla 3 works diferently in joomla 4. Previously there was no setting for height and width and the pop-up was shown in the article itself. Size of the pop-up followed automatically the length of the text. The pop-up you have now is in my opinion not the successor I have been looking for, unless you tell me which setting does the job.
Next I find that the button Modals does not insert the required code.
I copy the working code from an article and paste it in another I get the message 'Article not found'
I have tried to explain things. But it seems like you do not like Modals for Joomla 4.
You will probably want to use a different extension than Regular Labs Modals.
If you want a refund, let me know.