Oh dear, you are right. Massive oversight by me.
Outbound emails cannot be searched in VCC > Case Report. They are not interactions so don't show in Customer Experience > Digital Channels or Quality > Interactions. Awkward.
We are adding all our email channels as SMTP Servers (Config Manager > Security). When an email is sent using the SMTP instead of VCC Internal, the email also appears in the Sent Items for the email account which is pretty handy. We will have to use that for searching outbound emails.
Not being able to search for or report on outbound emails from VCC is pretty dangerous imo.