Canonical Technical Engagement Project Manager interview questions

I was contacted by the person who would be my manager with what looked like a template email and when I replied to have additional information (twice) she never reply. I was asked to submit an essay (a written interview, they call it) and perform two tests which took me some hours to be completed. The day after the submission I've got rejected with an automatic email. No real interview, no human interaction, no feedback on the results of the test. And they are looking for engagement!