The latest iOS 15/iPadOS 15 surprisingly brings the issue back to the original state in which the Alarm app doesn't make any sound when playing lossless music from Apple Music. On iOS 14.7/iPadOS 14.7, the Alarm app at least made the Radar sound, the default sound, when it realized it couldn't play the chosen lossless music.
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Models:
iPhone X running iOS 15
iPad Pro (9.7-inch) running iPadOS 15
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Btw, because of the ongoing issue, I purchased a HomePod mini as my alarm. Unfortunately and fortunately, because HomdPod mini hasn't supported lossless music, it can play any music in Apple Music.
Models:
HomePod mini running HomePod 15 (The Previous OS doesn't have the issue, either)