How to model spherical corners

Question

I am looking to recreate the object shown below but with a better topology. However, I cannot work out how I would model such a shape.

The important details I am trying to achieve is having the spherical corner be "tight" meaning the spherical curvature all happens around a section that terminates across 1 point on either side of the corner (green cross):
The closest method so far is the following:
Method

Select corner edge and bevel
Bevel the edges around the corner

Outcome
This is close, but it is very difficult to control the start and end point of the spherical section, because the end result depends on the depth of the first bevel.
The first bevel needs to be long enough to not cause the second bevel to collapse at the edges:

And even if you do get it close enough, there is always 2 extra segments that cause it not to be tight:
Is there a more precise and reliable method to achieve this spherical corner shape?

Jachym Michal · Accepted Answer

If I understand your goal, you can do this in one go.

Select all outer edges (even the horizontal one)
Bevel them with Clamp Overlap checked (Shortcut: C)
Merge double vertices (Alt+M > by distance)

How to model spherical corners

Method

Outcome

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