There are no direct ways of controlling autoplay, unfortunately. There are some general instructions here, although it will take some extra work to adjust those for this template (and will also require renaming and subsequent manual managing of the muted audio files whenever some would need to be removed from the collection).
But if you only have a single audio to autoplay on the backside (i.e. if there are multiple files recorded for the word audio, you are fine with playing only one of them) this can be achieved with a simple JS, that clicks on a specified audio button (as it will interrupt the autoplay of everything else).
For this, you’ll need to add some marking to set the section with the desired autoplay audio apart from the rest (I use “autoplay” class here, the “Extra 2” is supposed to represent your field with the word audio):
Then use it in a script to automatically click the first button in the section (add this to the very end of your backside template):
<script>
autoplayAudio = document.querySelector(".autoplay .soundLink, .autoplay .replaybutton");
if (autoplayAudio) { autoplayAudio.click(); }
</script>
If there are several audio files in that section, with a slightly different script a random one can be played back instead of the first as well. I’m also not sure if this will work well enough with the audio button animations, but depending on your preferences those should be manageable too.
Nice job on customizing the template, by the way. Looks good with that furigana and coloring!