There is a safe way and a risky way to do this, and the risky way is the one most people reach for first.
Cropped pixels are deleted. They are not in the saved file and there is nothing to recover. That makes cropping the most reliable way to remove something, and it should be the first choice whenever the sensitive part is near an edge.
Blur is the risky habit, for two separate reasons. The first is that many editors keep it as a layer over the original, so the covering can be peeled back off by anyone who opens the file properly. The second holds even when the pixels really are replaced: a light blur or a coarse mosaic over a short predictable string, an account number or a reference code, can be worked back, because there are few enough possibilities to render each one and compare. A solid block removes the information instead of scrambling it.
Check the whole frame, not just the part you were thinking about. Tab titles, notification banners, a name in a sidebar, an email address in a header. The detail you forgot is the one that gets shared.
For text such as an email address, a phone number or an account number, use the solid block. Small print under a light blur or a fine pixelation can sometimes be guessed back, and a block cannot. Blur and pixelate are fine for faces and for backgrounds.
Paint a little beyond the edges of what you want to hide, then look at the whole picture zoomed in before you save. The covered area is replaced in the saved picture itself, so it is gone from the file rather than hidden under a layer.
Less than people assume. Blurred text has been reversed before, especially for short predictable values. A solid block is safer.
No. Those pixels are not in the saved file.
No, which matters given what screenshots usually contain.
The solid block. It replaces the pixels completely, so the characters cannot be worked out afterwards.