You need to check "embed color profile". That's the checkbox just below "convert to sRGB". Both these boxes should always be checked.
If you do that, Export and Photoshop will match.
To get a match and a correct representation outside Photoshop, use only applications that support color management. A viewer like Windows "Photos", for instance, is not color managed and will not display correctly, ever, under any circumstances.
Whatever you do, don't change anything in Photoshop Color Settings.
If you still suspect something's wrong, you may have a bad monitor profile. If you're not using a calibrator, monitor/laptop manufacturers distribute their own generic profiles through Windows Update, and these profiles are very often inaccurate/defective. The proper fix is to use a calibrator, but if you don't have one, replace the current profile with sRGB IEC 61966-2.1. It won't be accurate, but better than a broken profile. Relaunch PS when done: