Under what circumstances to send a “you're welcome” email?
When you feel you should. There is no general rule for this in an workplace setting just like there isn't in a private setting either. As you say the vast majority of thank-you mails are perfunctory and should not be replied to. But people sometimes take the time to express their gratitude more profoundly and it absolutely makes sense to acknowledge that. You should simply exercise your own best judgement to determine when a thank-you deserves an acknowledgement.
When replying the key point is to keep it short and avoid inviting yet another response, unless you don't mind starting a personal discussion thread now that the business topic is out of the way. A lot of people tend to minimise their efforts or be self-deprecating when they're praised or thanked but try to avoid that and just acknowledge the compliment as-is unless there's a fundamental misunderstanding about your contribution that you should clear up.
As a general rule, you should never reply-all when sending a "you're welcome" mail. Only reply to the person or people that the thank you came from. In your case you could respond with something like the following:
You're quite welcome. I hope [whatever the next step they're taking now that your job is done] goes well.
It's as simple as that and you don't require anything more, but you can obviously personalise this if you know the people well.
Do keep in mind that etiquette rules never require that you acknowledge a thank-you mail, even it's very elaborate. Don't make the mistake of judging people for "not having the common decency to say you're welcome when they're thanked.".
