I can set the alarm on my iPhone on iOS 16.5 to any preset sounds, or ringtones, or any audio file in my Music Library, including synced/purchased/subscription music.
It should be possible for you as well.
Set an alarm on iPhone - Apple Support
How to set and change alarms on your iPhone - Apple Support
If ‘Radar’ is your default/last used sound, then tap that to change. On the page for selecting a sound, scroll up for a song selection. ‘Pick a song’ will further navigate to your music library from the Music app. Recently used songs will get listed as a menu option to make it easy to use it for other alarms as well.