Also (taking go as an inspiration), I (personally) find this very hard to read

Agreed. Go's implementation of errors as values is extremely noisy and error prone. I'm not a fan of it either.

You can always ignore an error return value and pretend that the “actual” value you got is correct.

Then that's a language design / api design issue. You should make it so you cannot get the value unless you handle the error.
I'm of the opinion that errors should be handled "as soon as possible". That doesn't necessarily mean immediately below the function call the error originates from, it may very well be further up the call chain. The issue with exceptions is that they make it difficult to know whether or not a function can fail without knowing its implementation, and encourage writing code that spontaneously fails because someone somewhere forgot that something should be handled.

The best implementation of errors as values I've seen is Rust's Result type, which paired with the ? operator can achieve a similar flow to exceptions (when you don't particularly care where exactly an error as occurred and just want to model the happy path) while clearly signposting all fallible function calls. So taking your example:

try {
  res = try_something()
  res2 = try_something_else(res)
  res3 = try_yet_something_else(res2)
  return res3
} catch (e) {
  // check which error it is and handle it appropriately
  throw_own_exception()
}

It would become:

fn do_the_thing() -> Result<TheValue, TheError> {
	res = try_something()?;
	res2 = try_something_else(res);
	res3 = try_yet_something_else(res2)?;
}

match do_the_thing() {
	Ok(value) => { /*Do whatever*/ }
	Err(error) => { /*handle the error*/ }
}

The difference is that you know that try_something and try_yet_something_else may fail, while try_something_else cannot, and you're able to handle those errors further up if you wish.
You could do so with exceptions as well, but it wasn't clear.

The same clarity argument can be made for null as well. An Option type is much more preferable because it forces you to handle the case in which you are handed nothing. If a function can operate with nothing, then you can clearly signpost it with an Option<T>, as opposed to just T if a value is mandatory.

Exceptions are also a lot more computationally expensive. The compiler needs to generate landing pads and a bunch of other stuff, which not only bloat your binaries but also prevent several optimizations. C# notoriously cannot inline functions containing throws for example, and utility methods must be created to mitigate the performance impact.