“Happy path testing” isn’t really testing at all. Following the “happy path” is a demonstration.
Here’s the role demonstration plays in testing: it’s nice to know that your product can achieve the happy path before you start to test it. To the degree a demonstration is a test, it’s a very shallow test.
If you’re building something new and non-trivial that matters to people, or that could harm people, there’s a risk that you might not entirely understand it or what it affects. To develop your understanding, you’ll probably want to test it; to learn about it; to investigate it; to interact with it directly; to probe it with tools; to stress it out. You’ll probably want to explore it and experiment with it; to evaluate it. That’s testing.
If you can’t even achieve the happy path, you’re not ready for testing.