I do not assume, that this document is anyhow compliant to the html5 or any other html standard.

But you are assuming that it isn't compliant. You could check by reading the standard.

See, for example, the html element:

Tag omission in text/html:
An html element's start tag can be omitted if the first thing inside the html element is not a comment.
An html element's end tag can be omitted if the html element is not immediately followed by a comment.

Is there a more strict validator out there, which reports every tiny deviation from standard html?

While tool recommendations are off-topic for this site, there are no deviations from standard html in the code you've presented.

The Nu validator is very good at what it does.

HTTP Error 500 is an Internal Server Error, so that will be their fault. Try validator.nu whilst you are waiting.

Maintainer of the current W3C HTML Checker (validator) here. I think it's important to understand the intended purpose of the current HTML checker, which is different from the purpose of the legacy W3C Markup Validator.

The purpose of the checker is documented at https://validator.w3.org/nu/about.html#why-validate:

The core reason to run your HTML documents through a conformance checker is simple: To catch unintended mistakes—mistakes you might have otherwise missed—so that you can fix them.

Beyond that, some document-conformance requirements (validity rules) in the HTML spec are there to help you and the users of your documents avoid certain kinds of potential problems.

There are some markup cases defined as errors because they are potential problems for accessibility, usability, interoperability, security, or maintainability—or because they can result in poor performance, or that might cause your scripts to fail in ways that are hard to troubleshoot. Along with those, some markup cases are defined as errors because they can cause you to run into potential problems in HTML parsing and error-handling behavior—so that, say, you’d end up with some unintuitive, unexpected result in the DOM

Validating your documents alerts you to those potential problems.

So as far as your question about "are better approaches to ensure contemporary standards-compliant markup", the answer is that it's not an either-or thing; there are a variety of approaches and the W3C HTML Checker is just one of them, and its goal isn't to be the single way to determine anything but instead to just help you catch mistakes you might otherwise miss and that might cause unexpected problems for your users.

As far as ways to get alerted to specific device issues or browser-implementation issues, we don’t have good automated checking tools for that, but a couple of things which are huge help there are:

• https://caniuse.com/ — detailed information about the level of support for particular web-runtime features in different browsers, and in different versions of those browsers, and in release of the browsers for mobile devices vs desktop

• https://wptdashboard.appspot.com/ — current test results across all major browser engines for dozens of web-runtime features/specs; if https://caniuse.com/ doesn’t have information about a particular feature, you can look through this dashboard and browse to the directory that has tests for that feature, and find whether a browser passes the tests for the feature

But as far as good automated tools we do actually have for checking other things, here are two:

• https://validator.w3.org/i18n-checker/ — W3C Internationalization Checker
• https://observatory.mozilla.org/ — for doing a security assessment of the content of your site