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There's no automatic expiration, no - I didn't think of that. I'll see if that can be added. For now, if you run delete localStorage.stackPronounAssistant_users in your browser console, that should purge the cache.
The site you're asking this on - Stack Apps - is community-run. The team that owns the sites might be looking, but I wouldn't want to bank on it - I suggest you ask them directly instead, since they're the ones who can give you authority (or not) to do this. Here's the contact form.
@TinyGiant I can add it to the list, but it's a fair amount of work for a relatively small gain. 6-8 weeks would be accurate, and add a couple for luck.