Good question, but hard ask...
I've not looked in a bit, but a few years ago there were some janky-ish chinese source/destination media converters that took in hdmi and used ethernet for A/V source in and out at the receiving end device. Some poking at the devices showed they just used ethernet and hard-coded ip's to talk between source and destination units, which if you adapted an interface of a computer to talk over, one could attach directly to the source unit and stream from using vlc for said source A/V feed, but hardly gets you the usb side of things too.
There are kvm hats for rpi's now too, so video in + usb to your pi, and then you can remote-control what it's attached to like a server, but not exactly a dumb extension as you'd just remote desktop to the pi and hit it's local app ui for the kvm, or via web hosted on the pi.
There is also usb-over-ip kernel features that have been around for a while, but I've never used them. Years ago Belkin had what looked like a usb hub with an ethernet port, say you'd throw that in some corner of your house without a pc, and maybe hook up a usb mic, and it had windoze drivers that made a remote usb device show as a local usb device to your system connecting to it. It was pretty broken with crap drivers circa xp era and probably the hub device too, but not seen anything like this in a decade and a half. I wish actually someone would again with modern linux and other os support.
There are poe hats for a rpi too, but it's still fairly limited what devices I see come with poe, and then of course you need poe switching at a suitable power output most of your older switches can't output over 15/30W of 48VDC.
I don't think you'll still find a magical one-for-all device out there as described, but I gave up looking purposefully long ago.
-mb