You may be able to use a "seatpost shim" that converts you folding bike's seat tube inner diameter to a different inner diameter. That way you would open up options for buying a better/different seatpost that actually has a modern clamp (mounting apparatus) at the top.
Your linked replacement says that post has an outer diameter (OD) of 34.1mm and 550mm long.
Maybe one of these "Wheels Manufacturing" shims could fit to convert it. There is one listed that is slightly off: it is listed as 34.0mm taking it down to either 27.2mm or 30.9mm.
Then, for example, there are 27.2mm diameter seatposts that are 400mm long that include the clamp apparatus at the top.
(I have not tried this setup before, so do not know it will work. Also, if the 400mm long seatpost would be too short, then this clearly won't work out for you. If you had the original seatpost pushed down much more than 150mm / 6 inches then it should work. It is a big difference between 400mm and 550mm.)