The focussing system of the Sony 6500 does not make differences if you use the viewfinder or the back display. However, there is one feature that could be the culprit:

The Eye-Start AF function: https://helpguide.sony.net/ilc/1640/v1/en/contents/TP0001273831.html

This starts the AF the moment you put the camera to the face. I have never used it, but it is worth a try to turn off if enabled. Note, that this is not the Eye AF feature, which focusses on the eyes of a subject in the image. It is just named really badly.

As you are in settings that should produce sharp results, the results are quite puzzling - to the point where it is difficult to figure out what went wrong.

At 1/1600 sec, 30mm and f7.1 the focus needs to be really off to produce this kind of softness. At a subject distance of appr 6m there is quite a big depth of field which should produce a reasonably sharp result.

This basically leaves these things that could have gone wrong:

• AF wide is choosing something in the full width of the image. It could be that the focus was really picking something that moved the focus out of the expected range. What is speaking against this, is that there is nothing critically sharp in the image. The twigs in the left area seem to be sharper than the fence. But again, then the focus is so off, that we cannot see what the focus plane was. And unfortunately, Sony does not save the focus distance to EXIF

• Depending on the settings, even with the 5-axis stabilizer in the camera, you can still have exposure settings where you create enough camera shake that the image is not sharp. At 1/1600 this should not be the issue.

• You could have theoretically have focussed accidentally before you raised the camera fully to the eye. If the finger still rested on the button, then the camera will not refocus due to single AF setting. However, this would be such a quirky edge case. It sounds as if you had your issue multiple times.

But be warned: I just confirmed with my Sony a7r IV that the green focus squares would not change after keeping the shutter half pressed. This can lead to the illusion that the camera has acquired focus even if the situation has completely changed. You should change the AF-S setting to AF-C and check if the issue is still there.

• This leads to the Eye Start AF... I am not sure if that is locking focus at all - but seeing all the clues, please turn off this feature if it is enabled. There might be a bug that it locks a single AF action which then looks like the focus was acquired, when it simply is not. On a second note: Eye Start AF might not even be available with a third party lens.

• Last option would be a very quirky defect of the camera or lens. You can never fully rule that one out.