I realised I do have one AER-capable PCIe 4.0 x16 slot - in my ASRock B650M-HDV/M.2 motherboard of all places! The MB is so sparse on peripherals that four of the CPU lanes are actually routed to slot 5!
(Image stolen from The Overclock Page.)
So I got that Kalea 2x MCIO card (via Ebay) and also a Supermicro CBL-MCIO-1240U2Y-E cable to try out:
The card is really a “Shinreal PCIe x16 to 2x MCIO 8i Adapter”, “XIC PE5160-4IL”:
I made sure AER was enabled and PFEH disabled in UEFI:
… inserted the card and hooked my PCIe Gen3 P4610 U.2 drive up. I had to disable MB Thunderbolt support which apparently is via some optional add-on card meant to go into PCIE3 (where the card was). A thing that threw me off at first was that the Supermicro cable has the wrong markings - the first port is the one marked Port1 and the second is the one marked Port0! 
Disappointing; you should do better, Supermicro!
Anyway, I booted up Fedora, installed kdiskmark and ran a benchmark on the drive while running ‘journalctl -f’ to catch any errors. Everything went fine!
The drive also linked up at Gen3 speeds:
# lspci -vv -s 04:00.0
04:00.0 Non-Volatile memory controller: Intel Corporation NVMe Datacenter SSD [3DNAND, Beta Rock Controller] (prog-if 02 [NVM Express])
Subsystem: Oracle/SUN NVMe PCIe 3.0 SSD v2 6.4TB 2.5-inch (P4610)
Control: I/O- Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx+
Status: Cap+ 66MHz- UDF- FastB2B- ParErr- DEVSEL=fast >TAbort- <TAbort- <MAbort- >SERR- <PERR- INTx-
Latency: 0, Cache Line Size: 64 bytes
Interrupt: pin A routed to IRQ 84
IOMMU group: 16
Region 0: Memory at f6f10000 (64-bit, non-prefetchable) [size=16K]
Expansion ROM at f6f00000 [disabled] [size=64K]
Capabilities: [40] Power Management version 3
Flags: PMEClk- DSI- D1- D2- AuxCurrent=0mA PME(D0-,D1-,D2-,D3hot-,D3cold-)
Status: D0 NoSoftRst+ PME-Enable- DSel=0 DScale=0 PME-
Capabilities: [50] MSI-X: Enable+ Count=129 Masked-
Vector table: BAR=0 offset=00002000
PBA: BAR=0 offset=00003000
Capabilities: [60] Express (v2) Endpoint, IntMsgNum 0
DevCap: MaxPayload 512 bytes, PhantFunc 0, Latency L0s <64ns, L1 <64us
ExtTag+ AttnBtn- AttnInd- PwrInd- RBE+ FLReset+ SlotPowerLimit 75W TEE-IO-
DevCtl: CorrErr+ NonFatalErr+ FatalErr+ UnsupReq+
RlxdOrd- ExtTag+ PhantFunc- AuxPwr- NoSnoop+ FLReset-
MaxPayload 512 bytes, MaxReadReq 512 bytes
DevSta: CorrErr+ NonFatalErr- FatalErr- UnsupReq+ AuxPwr- TransPend-
LnkCap: Port #0, Speed 8GT/s, Width x4, ASPM L0s, Exit Latency L0s <64ns
ClockPM- Surprise- LLActRep- BwNot- ASPMOptComp+
LnkCtl: ASPM Disabled; RCB 64 bytes, LnkDisable- CommClk+
ExtSynch- ClockPM- AutWidDis- BWInt- AutBWInt-
LnkSta: Speed 8GT/s, Width x4
TrErr- Train- SlotClk+ DLActive- BWMgmt- ABWMgmt-
Also AER seemed to be working:
# lspci -tv
-[0000:00]-+-00.0 Advanced Micro Devices, Inc. [AMD] Device 14d8
+-01.2-[04]----00.0 Intel Corporation NVMe Datacenter SSD [3DNAND, Beta Rock Controller]
# dmesg | grep AER
[ 0.269761] acpi PNP0A08:00: _OSC: OS now controls [PCIeHotplug SHPCHotplug PME AER PCIeCapability LTR DPC]
[ 2.335250] pcieport 0000:00:01.1: AER: enabled with IRQ 29
[ 2.335408] pcieport 0000:00:01.2: AER: enabled with IRQ 30
[ 2.335550] pcieport 0000:00:02.1: AER: enabled with IRQ 31
Conclusion: the Kalea-Informatique MCIO adapter + Supermicro CBL-MCIO-1240U2Y-E combo seems to be working fine at Gen3 speeds - even with the very long routing of the lanes on my motherboard!
(Unfortunately I don’t have access to any Gen4 drives, so I couldn’t test that. 
)