Just wondering is there PCIe 4x GPU-card for G5 Quad to get free PCI16x-slot for this:
...it might more fun use Classic with that than with HDD
Any sized PCIe card should work in any sized PCIe slot. This means you can connect an x16 GPU to a x4 slot. A riser is required if it doesn't physically fit. I don't remember if I tried moving the GPU to a different slot.
You'll often see a PCIe card or slot specifications mentioning the number of PCIe lanes physically and electrically.
All the slots in a Quad G5 are physically x16 but electrically x4 or x8 or x16.
Some PCIe cards are physically x4 but may be electrically x2. Some PCIe controllers don't support x2 so they may negotiate down to x1.
Quad G5 only supports PCIe gen 1 link rate. A gen 2 or gen 3 or gen 4 PCIe card should still be able to work. It will negotiate down to gen 1 speed.
My pciutils and directhw fork should be able to work in macOS on Quad G5. my pcitree.sh script will show the hierarchy of all PCI devices and show their PCIe link rate and link width.
I tried an amfeltec PCI Express Gen 3 Carrier Board for 4 M.2 PCIe SSD modules and a HighPoint SSD7505 (gen 4) in a quad G5 but that was before I finished the PowerPC version of pciutils and I don't remember which one worked.
Using one of them should be able to achieve full PCIe gen 3 x4 performance (≈3500 MB/s) in a gen 1 slot but I don't know if the Quad G5 can achieve that since I don't have any AHCI devices and no one has bothered to make an NVMe driver for Mac OS X 10.5 Leopard. I suppose a driver should be possible using code from NVMExpress.org or Linux.
Another idea would be to create a USB 3.2 driver which could support up to 20 Gbps. You would have to back port the GenericUSBXHCI.kext driver to Tiger or Leopard. I don't know if that's possible. The PCIe gen 3 x4 cards will only be able to do ≈800 MB/s unless you use a PCIe gen 3 switch such as from one of the M.2 cards or an external PCIe expansion chassis like the Netstor NA255A. I have one of those but haven't tried it with the G5. It might have issues.
A third idea is Thunderbolt. A GC-TITAN RIDGE should be able to work as a USB 3.1 gen 2 card. For tunnelling PCIe to connected Thunderbolt devices, some commands in Open Firmware before probe-all might be sufficient (look at Thunderbolt UEFI or Linux source code). Hot plug won't work without a complete Thunderbolt driver. USB-C DisplayPort Alt Mode or Thunderbolt Display might work with a DVI or HDMI or Dual Link DVI to DisplayPort adapter. I have a Gefen Dual Link DVI to DisplayPort adapter that can do 4K30 and 2560x1440@60Hz from my Quad G5 but I haven't tried connecting that to a Thunderbolt addin card.