Is it unethical to accidentally benefit from online material in a take-home exam?

I suggest that you don't lose a lot of sleep over something that happened several years ago. While you may have crossed a line, your description suggests it wasn't a bright line. Assuming your description is honest, you started out (probably) appropriately looking for alternate explanations of the material, not solutions to the problem at hand. But, rather than the internet it might just as well have been a different textbook.

But if it bothers you, then, assuming you are an academic, make sure that your own students get more explicit advice about what is and is not permitted.

It would have been better, of course, if you had pointed out the situation to the professor. But let the past be the past. Make the future better than the past if you are able.

It’s not unethical to accidentally benefit from anything, since the fact of such a thing happening is, as the word suggests, accidental. You didn’t mean to cheat, and it was the professor’s idiosyncratic testing policy that set up the perfect storm of circumstances that caused this “accident” to happen: note that the combination of a take-home exam and an in-class exam, and the way the two exams were scheduled, created a period of several days during which you were not allowed to search online for solutions to a specific set of problems, but during which you were allowed, and in fact incentivized, to look up general material related to the course. Hmm, I wonder what could go wrong with such an arrangement...?

TL;DR: no.

A take-home test is not, as a more formal test or exam would be, strictly a test of knowledge.

It tests the synthesis of your knowledge and resourcefulness in a fixed time frame, in all respects no different than an essay.

Anyone who gave a test of that nature should expect the student to make use of all available resources and only plagiarism to be unethical.