I haven't implemented this myself, so take with a grain of salt, but I think you should be able to handle this by writing a filter module that makes the field mandatory. I doubt a plugin ready-made for your use case already exists.
However, unless you can somehow validate the correctness of what is entered into the field (which you shouldn't be able to do for privacy reasons) I don't see much value in making such a field mandatory. IMHO, YMMV.
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April 20, 2021: Q2A 1.8.6 released!