You don't need to use base64. You can save the recorded audio in the Binary Data object directly to storage using the 'Set binary item' action. You can then load it again later with 'Get binary item', and once that completes the BinaryData object's 'Get URL' expression provides a URL to the audio data.
Normally you can't pass a URL directly to a 'Play' action. Instead to play a URL, use the 'Add remote URL' action to assign the URL a name, and then use the name in a 'Play' action.