Not terribly fast, I find inset + merge vertices + extrude to be an ok compromise: it follows the outer bevel profile exactly, but might not be what you want if you like to use less segments on short curve.
Sorry my bad, I just realised I never opened the first image you posted. In this case your corner can be thought of as part of a circle. Find the middle of this imaginary circle, place the cursor there, and then extrude along XY using the cursor as pivot. As always there are many solutions but no reason to overcomplicate it if it can be solved with a simple extrude
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https://images2.imgbox.com/b6/55/UfROeRPu_o.png
https://images2.imgbox.com/ef/65/qYtjKZSd_o.png
Need a bit of geometry clean up after extrude of course...