Does Messaging.SendEmail() not work in a Platform Event trigger context?

Limitation

Sadly, there is no apex email support from platform events. Per the documentation:

Sending an email message from a platform event trigger using the Messaging.SingleEmailMessage class is not supported. The email can’t be sent because the sender is the Automated Process entity, which has no email address.

Workaround

You can, however, send emails via email alert where the From Email Address is NOT "Current User's Email Address" but rather some other organization-wide email or default workflow user.

The reason, as outlined in this answer, "emails sent by the Automated Process user was "autoproc@YOURORGID" with no ".com" appended. This meant that Gmail would ignore it and the email wasn't being delivered."

In Apex, you might be able to use the SingleEmailMessage.setOrgWideEmailAddressId method to set the org-wide email and thereby the email be sent from a user other than the automated process user.