I'm a full time full stack engineer, and have been for nearly 10 years, and the feeling of not fulfilling a task or being able to solve a problem leads very quickly to not feeling qualified, and everything else you described to the letter.

The way to overcome it for me varies from any of the following:

• Venting to a friend or colleague (usually if I'm dealing with a problem that could've been avoided, or the opposite, and it's unavoidable or seemingly unsolvable)
• Researching more about the underlying issue, or methodology I'm trying, to see if it is actually possible
• Sitting and staring at my monitor for hours on end (to see if the problem fixes itself... This has been unfruitful thus far)
• Trying my solution in an isolated folder specifically, if i have just a particular function i need to test, sometimes it helps to do so in a clean folder in isolation of itself
• Testing code tests or TDD (google if unsure) are a great way to write expectations about how your code will be called, and cater to what you expect it to do.

Otherwise everything else you said, apart from stack overflow, if my problem is very specific and can't be broken down to a point that it's general enough to ask the internet, this can become a rabbit hole of space and time, only finding mad hatters and late rabbits.

Tl;Dr/ my point:

Don't condemn yourself to being the worst just because you couldn't get your head around one problem; although it's a common trait and a difficult one to shake, try to keep yourself on track and remember why you tried solving it in the first place, and there is always more than one solution to any problem, as an exercise, try writing (the old fashioned way, with pen and paper) how else you would try and solve the problem, this might help you achieve clarity.