Hello Mele,
Unfortunately there isn't really a way to do this with Arcade language, as this language is primarily used for controlling the way GIS features are rendered and labeled, rather than interacting with hyperlinked content. A list of the current available Arcade functions can be found below.
Arcade Function Index
https://developers.arcgis.com/arcade/function-reference/
There isn't really any available out-of-the-box functionality for validating URLs within an ArcGIS Online popup at this time. For a workflow like this, it may be more worthwhile to explore a workflow that involves exporting the table containing the applicant URLs from your webmap data, and running the URLs through a status checker website like the one linked below.
Bulk URL status code checker:
https://httpstatus.io/
I hope this information helps!
-TB