from your settings, it looks like it isn’t going to do anything. in AE, sRGB and HDTV use the same primaries so the color profile converter isn’t going to make any ‘burned in’ changes. Now, AE may look correct while you have it open because color management is enabled, which means your monitor’s .icc profile is being profiled/translated into your project’s monitor view.
Now, media encoder has its own color management as well. I guess it’s if you wanted to make another last minute change without changing your project file itself.
but here’s the thing, color management doesn’t do anything in other apps, even if its embedded if the other programs don’t understand color management. some can, but very few.
since you haven’t ‘burned in’ any color changes, any dumb program is going to open your image the way they see fit, which is usually sRGB translated through your OS’s .icc profile which may be wide gamut if MAC in P3 2.2 or something.
some people have said that changing the OS’ icc profile to rec. 709 helps things look what they want, but browsers, video players, etc. will still do what they want. VLC likes rec. 709 2.2 and quicktime player likes gamma 1.96. and different image viewers are all over the place what they like.