I just had a look again. On the 'Document Checklist' from UKVI that you can download when you finish your online application, there's no mention of 'Proof of Application' anywhere.
However, I just logged into the UKVCAS/Sopra Steria website and in 'Document Upload' there's a category under 'Mandatory Documents' called 'Proof of Application'. The description under it is customised to my own SET(M) application and says, 'Declaration signed by partner, The passport issued by United States of America for Mrs [my name here]'.
But the categories don't really make sense, because under the first 'Mandatory Documents' section called 'Proof of Identity/Travel History' it asks for 'Evidence of Mr [my husband's name]'s settled status in the UK, The passport or travel document for Mr [my husband's name] from British Citizen' but doesn't ask for proof of my own identity. But then, it looks like the scans they took of my passport at the UKVCAS appointment were uploaded into that folder/category.