A couple of thoughts. Is the phone in fact connecting by 4G instead of wifi?
If you have data switched on then it might actually be doing that but of course, I don't know anything about your coverage etc., but if the phone has data and wifi switched on and one fails it will switch to the other one without you knowing. If you find it is using 5g/4g then maybe you can get your own key for the mac? I think you are in America and I know data service can be very expensive for you there in some places so that may well not be an option of course.
Assuming that isn't true then it's odd that the computer doesn't get a signal while the phone does- which if I understand works ok? Well, you could try an external antenna for the Mac. I would think the one in the Mac is fine but it can help by being able to raise it higher or change its position and they aren't expensive.
Wifi reception is very position specific and things like walls obviously make a big difference but so do windows, mirrors, interference from other devices particularly microwave ovens, having the machine in a cupboard or closet.. The construction of the building has a huge influence and if it's modern and has rebar in the walls it's a natural Faraday cage and can be a nightmare for Wifi.
I doubt that getting another router will help you. I presume you are connecting directly to a repeater or router from the building? Adding your own router has it's own problems with bridging etc. If it has a good antenna then it may well get better reception but so will an external antenna for the mac with less conflict problems.
Another area to look at is the channel your machine is using to connect. If you have other people around you using the same service and a neighbour is using the same channel then you will have interference . Losing connection is usually interference. But also some channels simply work better in some buildings. I'm really rusty on this I'm afraid but you can change the channel and then see if the signal is stronger and if there is more or less noise.
(hold the option key and click on your wifi icon in the bar and it'll give you an advanced menu which will tell you what your bandwidth is, channel and if it's 2.4 o 5Ghz, noise etc.) There may well be an app that will help with this but I'm rusty as I say. 5ghz may work faster but tends to not penetrate walls so well. Your mac should do this for you of course but maybe you can help it.
If you want to check internet speed independently the best is fast.com.
It also sounds like the building has an inadequate service. Saying it doesn't work because people are using it isn't good enough. Maybe it's all very old and only uses very old protocols? You need more info to confront them with and it sounds like they need to upgrade their service.
I don't think anyone will be able to give you a complete solution but hopefully it's given you something which might help and very good luck
