Why do the arrow functions won't return "this" object in a jquery event handler?

Arrow functions are not identical to the function() syntax (function expressions). As you found, arrow functions do not rebind this. Sometimes you want that behaviour, but most of the time you don't. Personally, I try to avoid using this whenever possible. Too many gotchas.

Generally speaking, I think most people find the arrow function syntax to be much cleaner and more consistent. Though looking at the jQuery documentation, they do use the full function() syntax, so I'd guess that's the recommended best practice there. They're likely doing some rebinding behind the scenes.

You might need to move away from jQuery to fully embrace arrow functions. There's no need if it's working for you, but I will say that between fetch and document.querySelector, vanilla JavaScript basically has you covered now.

Whoever told you that they were just a modern alternative was just wrong, arrow functions have different semantics from function()s and don't bind their own this (meaning that this is equal to the current scope, which is currently window).

You could do this instead:

$("body").on("click", ".dome .btn", (event) => {
	console.log(".dome .btn onclick::");
	console.log(event.currentTarget);
});

I think your question has been answered, but I just wanted to say that the idea that arrow functions and traditional function expressions are exactly equivalent is a common misconception. It's actually one of the interview questions I commonly use for senior-level front-end/Javascript developers.

Arrow functions don't have their own this or arguments bindings (from this Stack overflow answer). I think your arrow function could be rewritten to return the element you want, but in general arrow functions should be viewed as throwaway helpers to perform a specific routine. They're more like operators and functional programming than object oriented methods and function objects.

Here's a link to the MDN page which covers arrow functions: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Functions/Arrow_functions