See this chart on Wikipedia: https://en.wikipedia.org/wiki/Roku#Feature_comparison
Assuming the chart is complete and accurate, any model listing "Stream to smartphone" under Audio/Analog should support private listening via the Roku app.
Roku Community Streaming Expert
I am not a Roku employee, only a user like you. Please, no support questions via private message -- post them publicly to the Community where others may benefit as well.
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Streaming Stick 4K+ 3821 | Streaming Stick+ 3810 | TCL Roku TV 43S245/C107X