I have created a Content Template for Media and created a Custom Field Group to add a custom URL field assigned to the Media post type, which I then added to the Content Template. I then filled in a working URL for a test image, and when I click on that image's attachment link, a page built with my Content Template is displayed, including the button with Dynamic Content link using the custom URL field. However, clicking on that button on the front end just re-displays the attachment page - the Dynamic Content link is apparently not really attached to the button...
I was able to reproduce this issue on my test website too and it seems to happen only when the "Buttons" block from WordPress is used on the content template for the default "Media" post type.
I've shared this with the concerned team and for now, you can use the Toolset's "Button" block, which correctly uses the custom fields URL.
( you'll see it added in your content template "Template for Media" )