No and no. No such thing as a “correct size” exists in the visual screen-viewing world. Folks can magnify or shrink images to their heart’s content. Let alone that they view on a screen with 72 ppi versus 96 ppi or other resolution. When your aim is to assure a one-to-one calibration of a certain physical dimension on your screen to be viewed at the same size on someone else’s screen, you should include a calibration bar on your image, for example as below.
You only need to resize screenshots when you want to reduce the time needed for a browser to upload your image from the storage location and for the user’s computer to display it (render it) on their screen.
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JJW