If you want to get good at something, practice that thing. It sounds like you're asking how to get good at coding interviews. So practice coding interview questions, not logic problems or competitive programming. LeetCode is probably the best known coding interview practice platform right now, and it has hundreds of free problems. In the LeetCode discussions, you can find people reporting on their interview experience, and companies often ask identical problems to the ones on the site. It's exactly optimized for what it says it's for.
You could get better at logical problem solving by practicing on Khan Academy or Brilliant or Art of Problem Solving. If that's what you want, then do those things. But it's not an efficient way to get better at interview questions.
> the group that's unwilling to put up with this is unqualified
Companies that get a lot of applicants care more about false positives than false negatives. So they're fine not hiring a lot of qualified people, as long as there's a low chance of accidentally hiring an unqualified person. Apparently LeetCode-style problems work for that type of screening.
You could get better at logical problem solving by practicing on Khan Academy or Brilliant or Art of Problem Solving. If that's what you want, then do those things. But it's not an efficient way to get better at interview questions.