Cat - N
You can use WiFi between devices without an internet connection of any kind, so internet packet transmission/control protocols (UDP and TCP..."TCP/IP (Internet Protocol) address", remember?) have to do with data getting where it's going (and it's condition on arrival)...'on someone else's network'...and would be spectacularly unrelated.
The issues with WiFi connections between routers and devices would be more antenna signal strength/range, radio channel used, if the router can and is distributing DHCP to internal devices...stuff like that.
Bless your heart, it sounds like you and I have the same modem and were talking to the same 'tech support' today (the many-th time for me...and 5 techs out to the house since April 22). I have finally rummaged through enough forums and found many complaints about the 'new modem' I was sent having a terrible antenna with extremely limited strength, yet they sent it to replace a completely wonderful, grandly working modem which they took with them, and, now, I can't print, and a whole bunch more...haven't tried the 15000 yet, but doubt I will be able to access it because this 'new' (crapola) WiFi router drops my iPhone 11 Pro Max at about 14' feet in a room where I could chuck the phone AT the router and break them both on impact. I won't even tell you some of the super stupid things I was told by 'front line tech support' today...egads!