I have an iPhone 11 and a new Ubiquiti UniFi 6 Lite AP. I can’t see any way to know from the phone (or the AP) if the phone is using a WiFi 6 connection or not.
IPhone – How to know if the iPhone device is using WiFi 6
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The wifi icon (click here to see how you could have found about it on your own) is the top bar, right between the carrier and the clock, and it replaces 3G or E. It looks like this: 
Like Alvar said, best way to be sure is getting in Airplane mode and turning wifi on.
As for youtube not working while others do, it's probably blocked. This could be on the wifi or on the iPhone, if it's a company phone with a provisioning profiles blocking it or if it's jailbroken and got a firewall on it. Just check if youtube works on any other device on the same wifi and you'll know for sure where's the issue.
If youtube is just running slow, but it is running, it could also be your other heavy sites are cached. Without more info I can't think of more options for that issue.
Do you mean to connect to the wireless router itself and get internet access this way?
According to Apple Support Forums,
Generally people will have a router establish the PPPoE connection and then share it with the devices on the local network.
Do you have a computer or another device already connected to the local network? If so, you might be able to share the connection off one of these devices as a separate Wi-Fi connection.
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Best Answer
In a nutshell, WiFi 6 is a marketing term for 802.11ax and the fastest way to know it’s working is to check radio details on the Ubiquity app and know exactly which encoding scheme is used from moment to moment. The radios adapt and steer traffic based on interference and other radios which change constantly.
Even with WiFi 6 available, if you’re stuck behind a slow router, a well engineered device might connect in a more power-efficient manner until it needs extra speed.
Both Apple and Ubiquity have a long track record of working together well - in the end, I recommend you look at the WiFi quality on Ubuiquity side and check your iOS device MAC address in the UniFi App and check your transmit rate / channel / RSSI to make sure your speeds are negotiating to the fast speeds you expect. As long as WiFi is faster than your server connection, it likely won’t matter if you’re on 5 or 6 flavor of the technical / marketing side of things.
To illustrate this recommendation:
I currently have a 802.11ac connection so the 866 MBps means I’m either running MCS 9 with two spatial streams and 256-QAM modulation on 80 MHz channels with 400ns GI or MCS 9 with one spatial stream on a 160 MHz channel and the other radio parameters the same. Since WiFi 6 includes older standards, you could argue I’m already using a WiFi 6 connection with my hardware for this specific answer.