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MP3-module from Aliexpress and some ESP-board with tiny display and micropython. Ten Euro.

You can make random search N in the MP3-module, because OFF/ON restarts and then you short NEXT-button wires N times.

You forgot to add /s. In no universe would this suggestion be at all practical, and meets practically none of the criteria I'm looking for.

Everything else is doable, expect maybe "lossless". But then, alas, WAV is as lossless as can be and memory is cheap.