No, unfortunately, that is not possible. Comments can not be automated in any way.

You could use Integromat to alert them via email when a field value has changed, but it won’t be tied to the comment field.

OK, thanks! Integromat seems to be a fully featured solution.

Is there perhaps a way to code it yourself then?

The comments area is not part of Airtable’s API. It cannot be programmed or changed or searched or integrated or automated in any way at all. It is completely off-limits except for manually typing stuff in there.