This may be due to the set preferences for the crop tool. With the Crop Tool selected, be certain the
Delete Cropped Pixels item in the Control Bar IS checked.
If this item is NOT checked, the file will no longer be a flat single layer file.
By retaining cropped pixels, you introduce a level of transparency. And since jpg does not support transparency, you can't then mere "save" to the jpg format.
Viewing your screenshot, the only layer is "Layer 0" and is not a flat background layer. The item above would account for this, but if the preference is not the issue....
....the "jpg" may not really be a jpg.
You may not be getting a flat background layer because the image is actually a png file or some other format with merely the suffix in the file name changed to "jpg". Actual jpgs open in Photoshop with one, locked, layer titled "Background".
If you wish to merely "save", flatten the image first. After flattening the image, "save" should work as you are expecting.
NOTE JPG is a lossy format - meaning to save file size (kb), the jpg format throws out data. Saving any jpg as a jpg reduces image quality. The more often you do this the worse the image gets.