IMO there's no one rule for intersections. How I handle each depends on traffic and overall conditions. If there's no traffic, I'd just go across the diagonal, maybe arcing toward the right so I was sort of riding with traffic flow, but not going to the corners. In heavier traffic I'd make the 2 corner maneuver you described (sometimes called a Copenhagen left turn).
If you want to be safe, use your common sense and ride as conditions dictate rather than looking for set rules.
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