If you wanted to connect your laptop to a desktop GPU, generally, you have to use a Thunderbolt 3-based graphics dock of some kind. However, a mod from Kosin (a China offshoot of Lenovo) has demonstrated that there is another way. Kosin shared a video where one of its employees managed to run an RTX 3090 off a notebook's NVMe M.2 slot, and it works! (via PC Watch.)
Kosin used one of its own laptops, the Ryzen 4600U-powered Air 14, to demonstrate its modification. The modder first removed the M.2 NVMe SSD residing in the notebook, then connected an M.2 to a PCIe adapter cable, allowing the RTX 3090 to communicate with the laptop. Finally, the modder drilled out a slot in the laptop's housing so the cable could run outside of the laptop's chassis.
Surprisingly, performance from the RTX 3090 was perfectly adequate, even with just four PCIe lanes being fed to the card. The system scored 14,008 points in 3DMark TimeSpy: For reference, a standard RTX 3080 paired with a Core i9-9900K gets 15,000 points. So, yes, you lose quite a bit of performance compared to installing the 3090 in a desktop PC, but the score is still quite good considering the notebook's specs (and the downgrade to four PCIe lanes).
If you want to do this yourself, beware that this is a mod and isn't guaranteed to work. However, NVMe based M.2 slots run off pure PCI Express, so theoretically, you can execute this mod with little to no compatibility issues.
Take a trip over to https://egpu.io/
Some laptops have two NVMe slots. It's definitely more efficient than thunderbolt, but the fact that you have to find a way to connect it seamlessly and you are reducing your internal storage potential makes it only a good solution for the edgiest of cases for an eGPU solution. Maybe if you are not planning on using your laptop outside of the desk at all or can modify it to connect it. Like I said it's SUPER edge case. I'd take the thunderbolt performance hit over this any day of the week over having to find a way to modify my laptop to do this while actually still being able to use it as a laptop properly. TB4 SHOULD be a little better since it can use 32Gb/s fully if the device is also TB4 controller but that's all theoretical right now there's no TB4 eGPU devices.
The 8x PCIe 3.0 connector on the new Asus Flow X13 is interesting, but it's proprietary and their only eGPU is sporting a 3080 Laptop silicon. Maybe they will expand that line with more laptops (16" 16:10 PLEASE!) and eGPU devices. If they released something like the LG Gram 17 with that connector on it (don't even put a dGPU in it.. just use iGPU) I'd buy it immediately.