How to make a pixel perfect adjustable outlined circle in Photoshop and also Illustrator, like, the one that Microsoft Paint has, as example?

How to make a pixel perfect adjustable outlined circle (with a simple tool so the circle can be readjusted and newly calculated later) in Photoshop and also Illustrator, like, the one that Microsoft Paint has, as example?

Like in Photoshop, I could go and use the Eclipse selection tool, remove the "smoothing" and apply a stroke. However, if I resize the circle, the circle does not recalculate, it resizes it on how the circle is, the circle stays the same with the pixels, which is an issue.

 

This is how the one in Paint looks like: https://i.imgur.com/GzrQlFv.png

In Paint I can use the tool easily without any problems.

 

And if I create a circle in Photoshop, I get this: https://i.imgur.com/1HAC5PG.png

So, yeah it’s like all blurry and stuff.

The same thing goes in Illustrator, however I found this comment https://community.adobe.com/t5/photoshop/pixel-circle-no-fade-no-fill-how-exactly-pixel-art/td-p/9627897#M143458

That says, that you can use the path of the circle and then apply a stroke by using the pencil tool, which makes it look correct, but I couldn’t find a way to do that, not sure what exactly he was talking about. But if that would be possible to do, it would be a possible solution because the circle would then be correct and can be adjusted and copied at any time.

 

Or is there a Photoshop extension, script for that, that adds the tool aswell?