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pipci.jeffgeerling.com/#other-cards

Has a list of cards that work.

BAR and arm64 have issues or no support.
For extra IO either mesa or the RIO project are best bet.

Not sure if this helps?

cnc@raspberrypi:~$ sudo lspci -v
0000:00:00.0 PCI bridge: Broadcom Inc. and subsidiaries BCM2712 PCIe Bridge (rev 21) (prog-if 00 [Normal decode])
Flags: bus master, fast devsel, latency 0, IRQ 39
Bus: primary=00, secondary=01, subordinate=01, sec-latency=0
Memory behind bridge: 80000000-800fffff [size=1M] [32-bit]
Prefetchable memory behind bridge: [disabled] [64-bit]
Capabilities: [48] Power Management version 3
Capabilities: [ac] Express Root Port (Slot-), MSI 00
Capabilities: [100] Advanced Error Reporting
Capabilities: [160] Virtual Channel
Capabilities: [180] Vendor Specific Information: ID=0000 Rev=0 Len=028 <?>
Capabilities: [240] L1 PM Substates
Capabilities: [300] Secondary PCI Express
Kernel driver in use: pcieport

0000:01:00.0 Parallel controller: MosChip Semiconductor Technology Ltd. MCS9900 Multi-I/O Controller (prog-if 03 [IEEE1284])
Subsystem: Asix Electronics Corporation (Wrong ID) MCS9900 Multi-I/O Controller
Flags: fast devsel
Memory at 1b80000000 (32-bit, non-prefetchable) [disabled] [size=4K]
Memory at 1b80001000 (32-bit, non-prefetchable) [disabled] [size=4K]
Capabilities: [50] MSI: Enable- Count=1/1 Maskable- 64bit+
Capabilities: [78] Power Management version 3
Capabilities: [80] Express Legacy Endpoint, MSI 00
Capabilities: [100] Virtual Channel
Capabilities: [800] Advanced Error Reporting

0001:00:00.0 PCI bridge: Broadcom Inc. and subsi

Use sudo with lspci, a lot of info is not accessible without it