I have an iPhone 13 Pro that I just purchased.
Whenever I load a YouTube video in my browser, whether that is using Chrome or Safari, every video I come across is automatically played in 320p quality by default. Using the cog icon I can change the quality to a maximum of 720p, there is no option for higher quality. However, on other devices watching the same YouTube video I can watch in 1080p, 4K, and 8K quality.
The App Store YouTube app does not appear to have this problem, however it is annoying having to use a separate app instead of the browser.
No other phone or device in my house has this problem, and I have checked the speed of my fibre internet.
Update to clarify question - How to get higher than 720p YouTube video quality when using Chrome or Safari web browsers. Especially when many videos outright refuse to load in 720p.