How can I embed unlisted vimeo videos via URL?

Hi all, grateful to any help or suggestions, if anyone else has run into something similar.

I have several unlisted videos uploaded via the video widget on my website. These were uploaded in 2020 or so.

When I try to add new Unlisted videos the video has a black screen saying the video cannot play due to my settings - and it only plays the video when I change the video to Public.

I would not like to have my videos public, is there anything I can do? I read somewhere you can use the code widget to embed the videos, however all my previous uploads did not require to be set up this way, and they are added via the video widget and work perfectly. I am wondering if there is something I am missing, and what the best route is to add unlisted vimeo videos to ReadyMag, and if the video widget is not viable, why do my older uploads still work fine?

Just curious as I would like to use a consistent upload method across all my videos to prevent anything breaking later on.
Thanks in advance!