Download a newer version ofSince Blender 2.91, you can boolean with new Boolean librarymanifold objects like a Plane.
I'm not just sure in what version 2.91 or 2There are two methods now.92 The ...
old 2.8xExact method should solve your issue
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It is cut out in inside normal direction (red color when Face Orientation overlay enabled).
If you still need to work in 2.8 you would have to use Solidify modifier or other tech to create non-manifold object as you mentioned.