If OP travels Polaris First on a 772 there is a storage area next to the seat on the side of the aisle. That's where I found the mattress pad the one time I flew Polaris First. It's big enough for a backpack in addition to the mattress pad.

In Polaris Business, the FAs never say anything about the small bag that my wife keeps in the small space where the feet go when the seat is in the lie-down position. Anything bigger has to go in the overhead bin.

I don't think that they allow a laptop to be kept on the lap during take-off and landing. An iPad, yes.