You could potentially put a 4.0 chipset on a 3.0 chip and it should nominally work, the chipset would provide 4.0 lanes to devices, but all the traffic would be multiplexed at 3.0 to go back to the chip so there wouldn't be a whole lot of point.
You could also put a 3.0 chipset on a 4.0 chip, which works fine and is even sensible for budget motherboards (this is how the AMD B550 chipset will work).
The things on the chipset tend to be slower devices that just need to be attached, not necessarily run fast. The chipset usually only gets 4 lanes total (so like, one NVMe drive saturates it) and hopping to the chipset adds latency which reduces IOPS on fast networking or Optane drives, reduces graphics performance for chipset-attached GPUs, etc.
[1] https://www.tomshardware.com/news/intel-stratix-10-dx-upi-cx...
Nominally QPI/UPI but those protocols are not hugely distinct from PCIe in general. AFAIK it’s basically PCIe but encrypted, so that nobody else can replicate their chipsets (like used to happen in the old days with nForce/etc).
Also your numbers are off, easy rule of thumb is that one PCIe 3.0 lane is one GB/s of bandwidth per lane. So 3.0x16 is 16 GB/s of bandwidth.
So it just needs 8 GB/s of bandwidth to run at 4.0x4 speeds.
On HEDT and modern server, (2066 and friends), only about 8 of the PCI-E lanes come from the chipset, and the rest come directly from the CPU. The QPI and it's successor UPI is used to connect CPUs to each other, not to a chipset.