A modder on Chiniese video site Bilibili has successfully created a DIY expansion card for the Xbox Series X and S. This mod potentially allows you to use any PCIe 4.0 SSD as expandable storage for the consoles -- like the PS5 allows -- and bypass purchasing one of Microsoft's expensive expansion cards built by Seagate.
To make the card, the modder first tore down an Xbox Series S and a Seagate expansion card to see the internals of the built-in drive and the expansion card to understand the console's storage requirements. She confirmed that the consoles do run on NVMe, but each drive slot has different PCIe protocols: one for the built-in drive and one for the Seagate expansion cards.
There are two protocols because Microsoft's expansion cards use a modified version of the CFExpress, a popular removable media protocol that's very common in the photography market. The nice thing about CFexpress is that it natively supports NVMe, meaning you can make fast, speedy NVMe drives that are designed to be removable, like USB thumb drives.
So the modder went to work and installed a custom CFExpress card that supports PCIe 4.0 speeds and paired it with the internal SSD of the Xbox Series consoles, the CH SN530 M.2 2230. This SSD is an OEM, PCIe 4 x2 drive that perfectly meets the requirements of the expansion slot.
Once done, her Xbox and the card worked perfectly, with the card showing up as a usable device in the Xbox menu.
Despite this modder's success, this mod would be very difficult to duplicate with other hardware. The PCIe Gen 4 requirements are completely proprietary to Microsoft and its Xbox Series consoles since the official CFexpress standard only supports PCIe Gen 3 speeds or slower. Also, finding a PCIe Gen 4 drive with just two lanes is nearly impossible.
The modder hasn't yet tested PCIe Gen 4 SSDs with 4 lanes, so it's possible that the right CFexpress card could automatically disable two of the lanes.
If you're wondering about your best SSD using PCIe 3.0, you're out of luck. Other Chinese modders have tried installing a Gen 3 CFexpress card into an Xbox Series X/S console and were met with an incompatibility prompt.
So, for most people, this mod will be completely inaccessible, thanks to Microsoft's use of proprietary hardware. Maybe one day, someone will find a way to bypass these problems, but for now, your best option is buying Microsoft's official expansion cards for the Xbox Series X or S.