Personally I think the new Music App in iOS 13 is really good looking app and very simple to use, specially in dark mode. The problem that I have is the shuffle mode, I keep hearing the same songs, maybe 20 in a collection of 3000.
For that reason I've been looking for a replacement. What I found was Flacbox, it does not require the the Music App and it plays what ever you through at it. It's free with ads and $5.00 to remove them.
The other app that I like is Marvis, it requires the Music App to load the songs and has a great design and lot of features, in shuffle mode is great. It costs $5.00.
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I have the same problem.