I’d suggest some consideration and practice with debugging and troubleshooting, which will be beneficial in amny contents such as troubleshooting, and eventually as part of your efforts toward learning to program amd app development.
In the case of that link and related debugging, try downloads from somewhere other than Google, and other than from Google search results. This because Google does all sorts of “creative” stuff with links, routing many of those links back through the Googleplex. (This is one of various resons why my use of Google has been decreasing.)
To test and debug basic operations of a web download on an iPhone or iPad, try using DuckDuckGo or other such search engine (who do not generally insinuate themselves into links), download an mp3 file from somewhere widely available, and unlikely to involve DRM such as, say, Wikipedia or such. Here’s one such Adune.mp3 example. From that Wikipedia webpage, there’s an Adune.mp3 link shown just below the black playback bar, and tap-and-hold on that link gets the following pop-up (below) and the download (green highlight) works, and the downloaded file can be played from within Files app.
Again, if you are having issues with Kapwing and whatever Kapwing is (or is not) doing, contact Kapwing support.