ᐅ Basement - How to Insulate the Floor?

Hello,
we have a concrete floor in our basement, which the previous owner modified by adding a structure with 80 joists and 25mm (1 inch) OSB panels. The space in between is currently filled with air.
The house was built in 2006, and the basement is a waterproof concrete shell ("white tank") that has been insulated from the outside.

I would now like to convert my basement into an office and am considering whether it would make sense to fill the space between the floor and the OSB panels with insulation material. The plan is to install laminate flooring on top of the OSB panels later.

In the attic, I have some rolls of stone wool and glass wool, as well as a few insulation boards. Are these suitable for this purpose? Do I also need to install something like a vapor barrier? The basement itself is dry!

Thanks and regards,
Thomas

For a house built in 2006, the basement floor should already be insulated from the outside.
What is the purpose of the construction with the beams and boards? To save on the screed?
In my opinion, adding more insulation doesn’t make sense.
Is the remaining ceiling height sufficient? This unusual floor construction alone will easily add about 10cm (4 inches).

apokolok schrieb:

For a house built in 2006, the basement floor should already be insulated from the outside.

According to whom? I claim that the basement walls have external insulation, but there is no external insulation underneath the basement floor slab.