I’m a landlord with a couple of small blocks of flats. Converted/built before the need for noise testing but built to the standard applicable.
My experience has been that if you have “hard” flooring you’ll always get noise transmission. I used to use a very heavy rubber crumb underlay under laninate floors, this helped. In one flat i laid rubber crumb , 12mm mdf rubber crumb then the laminate. Made a considerable difference but it just meant tenants had less to complain about rather than solving the issue.
In another flat i put up a secondary ceiling on decoupled rubber mounts metal channels, insulation same on 2 walls for flanking sound.Again better but still have issues.
Biggest problem is bedrooms below another room usage, people are far more sensitive to noise when resting/sleeping.
Doing away with a hard flooring and using a decent carpet will make far more difference than any simple underlay product.
Never underestimate the amount of noise transmitted down flanking walls.

Do we put a relatively lightweight 'acoustic' quilt in the void above decoupled ceiling, like in a speaker cabinet, to absorb/damp air pressure-waves?

My preference is RWA45, the more you get in the better, but you need an air gap. But attention to detail and ensuring there are no continuous pathways are more important. Two layers staggered seems to be worth the effort.

However if sound transmission is expected to be a problem then dealing with a design it at the earliest possible stage in a build / conversion is best. Retrofit later can be pretty hit and miss. In addition most peoples expectations are far greater than the actual results achieved.

I’ve used these people for the genie range of products,

https://soundstop.co.uk/

Lots of products to consider.

My most problematic flat has a bedroom in a basement flat beneath a kitchen and bathroom above. I’ve eventually realised i’ll never keep up with the increasingly sensitive tenants of today (as against 15 years ago). Once the tenant in the upper flat leaves, the flat will be rejigged to move the kitchen and replace it with a bedroom. Flat was converted 22 years ago and ready for a refurb , plus the revised layout will be better suited to tenants now seeking to live in the area.

As a bit of an aside has anyone used the SBX phonestar boards? The idea sounds good but at a cost of around £90 to be equivalent size wise to a sheet of plasterboard, I couldn’t justify the expense in the absence of some real world (independent) feed back.

Looks like a very interesting product. I see there is a slightly cheaper British-made product branded DBX (I thought that was an audio noise reduction system?)

Thanks for the recommendation of "Soundstop", i don't know why my internet searches directed me elsewhere. They seem to have some possibilities that aren't chopped up car tyres.