I've had several customers where I discover their entire apartment is on a double NAT AND on a shared LAN.
Typically, its not that awful, but there are also lots of landlord specials that use crappy repeaters or the building is locked to a shady contract and you can't do anything to get better service.
If you are renting a room, the “complementary WiFi” is likely the homeowners router and you're at mercy of that setup.
Wifi and cellular internet can frequently provide subpar experiences that are sensitive to jitter and packet loss such as video games or voip.
tldr, you might have a hard time getting your own internet service. Before you sign anything, try testing it with this tool. https://speed.cloudflare.com/
So, that test I posted also shows the condition of the connection. Not sure if your tests also had that.
Your concern is warranted, the nature of the connection can be difficult to determine. You could use a home router setup to connect to a trusted endpoint such as a VPN service. That would help you avoid immediate concerns, should that not be possible due to aggressive filtering methods. I wouldn't sign that agreement, but if forced to do so due to circumstance you could work with your company's IT department for a suitable solution, and for personal look into network privacy tools. https://en.wikipedia.org/wiki/Overlay_network