You'll have collectively said "do fidem". The rest is read by the official at the table, not the graduands.

The question as to whether this constitutes swearing an oath or making a simple promise was an interesting one for me as Quakers traditionally refuse to do the former.

"i give my trust". i believe that would be a promise or affirmation as it does not invoke a god. Unless it's the accusative of the goddess of faith (unlikely).