I looked into whether I could expose my NAS storage to PS5 & XBox. Turns out that it's possible! It's possible by mounting the NAS shares over iSCSI or NFS, and then emulating a USB storage device using the g_mass_storage module that exposes said storage to USB hosts.
Besides time and cost, one major blocker for me right now is the bandwidth that such a system would provide. It's just not that big of an upgrade. Raspberry Pi very famously supports USB-OTG (similar/same as xDCI), but it only does so with USB 2.0 speeds, and so do all the other SBCs in that class that I found, except for one, RockPi4. RockPi has a Gigabit ethernet port, so if you max out ethernet, you can provide stable HDD speeds to both the PS5 & Xbox.
It would be really interesting to explore a solution where you have the ability to plug in a custom PCIe network card (or an express card) that lets you go beyond 1gbe because then you can really saturate the USB 3.0 interface.