Will a NVMe<>PCIe gen3 x4 (physical x16) Adapter use x8 of PCIe gen2?

I've found a couple of x16 nvme adapters like those:

https://www.amazon.de/dp/B07VV9DYTL/ref=sr_1_2_sspa https://www.amazon.de/dp/B07RWCGP1S/ref=sr_1_8

So as a follow up to my earlier question PCIe gen3 x4 card in PCIe gen2 x8 slot - full performance possible?:

If a gen3 card that has physical x16 but only uses x4 (gen3) is put into a gen2 slot, would it use x8?
Or is that x16 just marketing and perhaps a means of holding the SSD in place more firmly than a x4 slot would?

Solution 1:

The "x8" and "x16" on that adapter is just there for mechanical support and/or marketing, you can see this easilly just from looking at the PCB, there are no traces going to those pins, some pins are missing and the sections are designed to be broken off!

In principle an adapter with a bridge chip could exist, but I have never seen one.

While I have never seen a single drive adapter with a bridge chip, there do apparently exist multi-drive adapters with them. For example the SSD7101-A from Highpoint, not cheap though.