"insufficient access rights on cross-reference id" error on flow email alert

I am suddenly getting the "insufficient access rights on cross-reference id" error in a flow that was previously working when trying to send an email notification (workflow email alert/email template).

I am not sure why I would get this error since it is not a DML operation.

I figure this must be a user permissions/sharing issue, but how do those relate to alerts or perhaps email templates ?