Oh dear. Noise abatement requirements with hard surface flooring over light weight concrete (aka "gypcrete"). And you only have enough room for 6mm worth of acoustic insulation. Hmmmm. You are getting into expensive territory.

First check what is ALLOWED by the HOA/Condo board. They will have ratings that will tell you what you have to MEET or exceed with hard coverings.

Secondly check to see if the acoustic glue underlayments will even grab gypcrete. Most things HATE gypcrete. I mean HATE. There are many high-quality glues that do NOT grab gypcrete. And the one's that do, can be nasty. But don't worry. Being in California means you can't purchase anything that violates CARB compliance - unless you order it over the internet (ahem...best to stick with brick and mortar point of purchase for stuff like this).

And just for fun, not all wood floors can be floated and not all can be glued. And not all glues grab gypcrete...see where we are going here?

And then there is the noise abatement that MUST be addressed BEFORE you go any further. Without those numbers, you are flying blind and so are we.

In the cork industry, I NEVER got my 6mm cork underlay to pass a SoCal condo boards requirements. My customers ALWAYS had to go 12mm with a wood floor (of any kind).

You can get some decent sound reduction with mass loaded vinyl. But it is expensive. It is very thin and very expensive. And vinyl does NOT like sitting underneath wood. But it depends on the mass loaded vinyl product.

And QuietWalk Plus is a product that is relatively thin and yet has some of the same acoustic insulation as 12mm cork underlay. It will save you the height at least. It too is not cheap.

https://www.mpglobalproducts.com/flooring-underlayment/products/quietwalk-plus/sound-rating/

You cannot glue onto lightweight (under 2500 psi) concrete - float only. There is a 3500 psi minimum rating on adhesives.

Thank you for your advice and expertise! The HOA surprisingly doesn’t have regulations on sound insulation. The Board is looking into some rules on that regard but currently only a handful of units are grandfathered in with hard surface floors. (We previously had parquet flooring that was glued directly on the lightweight concrete.)

So it seems our solution would be to float the floor and use either 12mm cork or the QuietWalk Plus? Any other underpayment products that offer similar sound insulation?
(I will check with the contractor if 12mm is ok to use after all).

Thanks G&S...I knew there was a limitation but I didn't know what it was. That helps!

For the thickness, I would look at QuietWalk Plus. As much as I love my cork, I know the numbers for QuietWalk Plus are equal to 12mm cork underlayment. In your situation, that makes it the perfect underlayment for your situation.

And floating a floor is a good idea over light weight concrete. The only issue is PATCHING the gypcrete. It is a pain in the butt! Like a real hassle. The flooring contractor has to have knowledge of gypcrete patching. That's the FIRST question I would ask.

Update: our flooring guy insists the floor needs to be glued. (Although this floor per the manufacturer’s installation guide can be glued, floated or nailed). The flooring guy is telling us we need to first glue the underlayment to the gypcrete and then glue the flooring to the underlayment.
Is this possible? Are there any glues that secure underlayments to the gypcrete? Or is this a labor and material up-sell?

NWFA and adhesive manufacturers "Do not allow" a glue down over a minimum compression strength of 3500 psi - "Float only". You will need to find out more information about your slab before you risk the chance with a glue down floor. A 1" thick, light weight slab is trouble for glue down. Find out which adhesive your flooring contractor is using and read the mfg's "TDS" document. The information is in there. Make sure s/he is following the mfg's installation guidelines. Otherwise, find someone else to do the install - properly.

A double glue-down installation is possible if, the mfg's guidelines are met.