Hi:
I can't say why the card isn't working in the PCIe x1 slots.
I have several HP business desktops with PCIe x1 wifi adapters installed and they all work fine.
See if this works...if your PC's white PCIe x 4 slot is free, see if the card works in that one.
That is the slot that looks just like the black PCIe x16 slot.
If the card doesn't work in that slot either, return it and buy the Intel desktop AX 200 wifi kit instead.
Amazon.com: Wi-Fi 6 (Gig+) Desktop Kit, AX200, 2230, 2x2 AX+BT, vPro: Computers & Accessories
Chapter 2, page 12 of the Hardware Reference Guide indicates your PC has a M.2 slot for a wifi card.
Hardware Reference Guide (hp.com)
The only thing you may have to come up with if it is not included in the kit, would be the M.2 wifi card hold down screw, which is probably a PM2 x 3mm screw.