Bicycles - standard, folding and disassembled - travel free in
non-peak periods. You will need to purchase a child ticket as well as
your own if you wish to travel with a bicycle between the hours of
6.00am and 9.00am and 3.30pm and 7.30pm on weekdays.

to me that makes it clear that a "bicycle" includes a folding one,
even folded.  So presumably a large backpack is OK but a folder in a
bag is not...  It also appears that a bike in a bike bag or box is
also banned on peak hours, but a bar fridge would be OK.

I suspect that most staff would not care about a folder in a bag, but
might care about one out of a bag.

I have been asked to show a 2nd ticket for the 'bent towards the end
of evening peak, but being a disgustingly law abiding type I had
bought one.