Background Info
I have a quadriplegic client who lives in a hospital (long-term living) and has his own room. He has a laptop running Windows 11 and an HP printer. The hospital provides WiFi for the residents, but I believe it's a bit more locked down than your average household WiFi router. Normally, computers can find printers on a LAN without any issues, but this situation is proving to be a bit more difficult. I've successfully connected the printer to his computer via the HP Smart app (which seems to be the only way to do it with HP nowadays), but only by manually entering its IP address.
The problem is, the printer isn't connected to the computer anymore after only a couple days. I think it's because the printer's set up via DHCP so it's getting a new IP address after a couple days and not being found from the computer anymore since I had to manually enter its address. I tried setting a static IP address on the printer, but for some reason, it isn't accessible on the network as soon as the changes are saved (note: the subnet and default gateway were correct when attempting static IP, and the IP wasn't already taken by another device).
Question(s)
My first question is this: Can the computer not find the printer automatically because it's on a hospital network, which is likely more strict than household networks?
If so, my main question is, can we use a separate router to act as a "household" network for all of his devices, and still get uplink from the hospital WiFi? If we can, how exactly would we go about this? Keep in mind, we don't have access to any physical hardware like the router itself or any cables, it would need to get an internet connection wirelessly (like a booster/bridge?), but also provide its own network.