Other than Americans wanting to feel superior (no offence intended, I'm sure most countries want to feel that when possible!) is there actually any public evidence that's the case?

Even when it comes to superiority of physical military forces, different people (with a range of different biases) have different opinions on stuff like whether a hot, all-out (but non-nuclear) war between USA and China would prove one or the other to be stronger, and while you may read that and think "I know which side is better and anyone who disagrees is just buying into delusional propaganda" at least to form that view you've had the ability to follow a lot of publicly available details on military developments over the years, learning about current and next gen fighter jets, drones, ships... etc.

But when it comes to cyber stuff, both offensive and defensive, it's generally a lot more secretive in terms of stuff that's actually been done (see for example the speculation in this thread that US power grid failures in recent years might have been caused by foreign adversaries - there's no evidence that's true, but if the US and China had both spent the last decade trying to take offline as many of the other country's power grids as possible we likely wouldn't have heard about it). Yet alone for hypothetical but saved for war capabilities. If a hot WW3 broke out tomorrow, who actually knows what hacking tools any country (from superpowers to smaller players) actually has, waiting to be used? Presumably they all spend a lot of effort trying to learn about each other's capabilities, and maybe they're successful enough that they actually do all know most of what everyone else can do - but they don't then announce that the way we hear about North Korea testing a new missile or about America developing a new fighter jet. I feel like we the general public just have no idea how advanced or not wartime capabilities might be. Am I wrong? (I may well be, as I'm in no way an expert in this field; I just believe that things like the document you linked are massively influenced by both the politics of the authors and the information available to them.)

US cyber capabilities have an edge because they can analyze all of our data stored with US tech companies and they have interception points on all major internet cables.

Their human intelligence is much better prepared to "convince" someone to act against their own interest if they can look at your last ten years of communication, family pictures, and web browsing history before they even meet you.

Imagine working in a foreign country where death penalty is applied to certain crimes, like blasphemy or homosexuality. They just need to find one person in the target organization who has a secret twitter account that talked badly about god and then they hit them up and tell them to plug in a certain USB stick to a certain system. Cyber operation succeeded because they have a shell.