Cat 5e is fine for Gigabyte speed though, it's old but that isn't the issue here.

@Bandorr There's a free app you can get for android called Wifi Analyzer, you could install that and fire it up you get a very good visual representation of the wifi networks around you, they should all fall into the channels of 1 - 6 or 11 if using the 2.4ghz network but if you open that and see that your network and every other network in your area are all wallowing in the 1 channel but there's nothing on channel 11 for exp just go into your routers wifi setting and find the channel setting and change it over to the one which was least busy in the wifi analysis, note that while you can pick any channel number you should only use 1-6-11 for wifi etiquette sake as those channels when used do not overlap each other.

If you are connected to your hotspot using 2.4ghz wifi btw your max speed there would be in the region of 50MBps as that is a limitation of 2.4ghz wifi, while you can get faster speeds on 5.0mhz the range of that frequency is less than that of 2.4 so a lot of devices can just default to using the 2.4ghz as a standard especially if they're moving back and forth from the router, if you really want great wifi you could look into getting something like a unifi wifi AP for your house/apartment, those things are monsters for getting great signal in a large building.

https://www.amazon.co.uk/Ubiquiti-Networks-UAP-AC-LITE-Access-Point/dp/B016K4GQVG/ref=sr_1_3?keywords=unifi+wfii+ap&qid=1569388118&s=gateway&sr=8-3-spell

Those are some serious pieces of kit but you won't get a better wifi AP in my opinion.

Are you talking about LAN or WAN throughput? Wifi is a different beast, depending on your environment 30mbps might be the best you can get.

For LAN throughput check review sites about your router. A gigabit interface does not mean gigabit throughput.

If it's about WAN throughput you will have to accept that not every server on the internet will give you 1gbps.

You have self-organizing network enabled. That might be part of the issue with Wi-Fi, oddly enough, that's why you can't see a second SSID. That's assuming the problem isn't congestion or interference, though they most likely are. 

You can disable SON if you access your routers' portal (192.168.1.1. or router website suggested by AT&T) or by calling your provider. Worth trying. 

Is the issue with Wi-Fi happening even if you are close to the router, btw?

If the B is ever upper case then it's talking about a Megabyte as in when a movie is 700MB, the lower case b is a Megabit which is 1/8th of a Megabyte no storage ever really measures things in Mb, ISP's tend to sell stuff using Mb because it sounds like it's 8 times more when all it does most of the time is cause confusion that people aren't getting their full speeds.

If you're living away from others though wifi conjestion isn't going to be your major issue.

One thing I would say though, is that you're talking about the Switch at a point, you know that the Switch has a notoriously bad Wifi adapter in it, but there are things you can get to stick into the dock to connect a normal ethernet cable into the dock so you can get faster speeds when docked (if you're playing an online game when you drop the Switch into the dock it will remain on wifi until you close that game and reopen it, the symbol for Wired network is completely different up near the battery so you can tell that way) but the Switch is awesome for being able to use standard usb ethernet adapters, Nintendo did really well with how 3rd party peripherals work so easily with the Switch.

https://www.amazon.co.uk/UGREEN-Ethernet-1000Mbps-Compatible-Nintendo/dp/B00MYTSN18/ref=sr_1_3?crid=KR22OKHA1DGV&keywords=ugreen+ethernet+adapter&qid=1569474746&s=gateway&sprefix=ugreen%2Caps%2C135&sr=8-3

Something like this from UGreen is what I use.