Nice, I didn’t know about this feature. For others who have a hard time finding it:
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Enable config setting “email in” under “☰ → Admin → Settings → Email”.
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Go to “☰ → Admin → Groups → <choose group> → Manage → Interaction” and set “Email: Custom incoming email address”.
(This setting is not visible before enabling “email in” in the previous step.)
If the OP wants the email to message inbox feature only for a few users (say, staff members), it will be acceptable to configure it manually for each of these users. Then, the above technique together with groups with one member only are a suitable option.
The “custom incoming email address” of each group can still be set in format “Discourse username @ my Discourse domain”.