That Palm keyboard you’ve linked to brings back so many memories! I also had one and it was definitely transformer like and very much mechanical and bulky 😂.
I don’t type on the foldable keyboard directly on my lap because of the middle fold as you’ve pointed out. It is also awkward to have a phone on my lap because of the viewing angle.
I try to do a quick ergonomic set up: place the phone on an arm rest of the bench and away from the keyboard. Then prop the phone up with a ring case. Finally, I would lay the keyboard flat on the bench itself.
Unfortunately not all park benches have arm rests so that might not work everywhere.