The metadata is thinner, but not empty
A screenshot is generated by your operating system, not a camera, so there is no lens or GPS data. What you often do get is the capture timestamp, the display resolution, the colour profile, and on some systems the software that made it. PNG screenshots can carry text chunks written by whatever tool touched them afterwards.
Editing a screenshot adds more than it removes
Open it in an image editor to annotate or crop, and that editor writes its own metadata block on save: its name, its version, sometimes a document ID, sometimes the registered user. A screenshot that started clean can pick up your name on the way out.
The real leak is inside the frame
Notification banners, browser tabs, the account name in a corner, an autocomplete dropdown, a reflection of a second monitor, the file path in a title bar. No tool can strip these, because they are part of the picture. Look at the whole frame before you send it, not just the part you meant to capture.