As already established, export as sRGB - whether or not you embed the profile is really moot, as with no profile, sRGB will be assumed.

Prior to that work in whatever you got from your camera*. Only convert once at export.

The major error, however, is to use Proof Colours with your Monitor profile. This will apply a double translation & generally look horrible, or you 'fix' your image to look right like that & it will look horrible everywhere else.
You really don't ever need to use Proof Colours in an RGB workflow if your only conversion is right at the end. It will be as close as it's possible to get.

So long as your monitor's profile shows in the list [not chosen, merely available] at Colour Settings > Working Spaces:RGB then your system is aware of it & will apply it already to Photoshop's display output. Here you should set your Working Space to sRGB, then ignore it, you're not really going to use it.
Set Colour Management for RGB to Preserve Embedded Profiles. That way your camera profile will be used right the way through your workflow until your final export.

This, of course, all assumes your monitor is correctly calibrated beforehand, that the icc profile is being used by the system & that Photoshop is aware of it.

*You can probably choose in your camera ahich profile it will work to internally. Mine will do sRGB or Adobe RGB 1998. Some will do ProPhoto, which you have to be careful of because very few monitors can actually display it. I use the Adobe 98 as my monitor can display it accurately. I'd be hesitant to insist you photograph at sRGB if that's all your monitor can support, as you may be missing out on some small aspects of the potential gamut, but you wouldn't be able to see the differences yourself anyway if the monitor can't display them.
Most monitors these days can display 'most of' sRGB, only premium displays will be fully capable of Adobe 98 & very few high end can achieve ProPhoto.

One last trick, in case you ever enable Proof Colours by accident [it's right between Transform & Hue/Sat, so it's not impossible to do] - set your proof profile to sRGB, then you won't wonder what the heck happened later ;)

…and a late thought - most consumer-level printers these days want sRGB images anyway, not CMYK, so you won't even need Proof Colours for those either. I have two regular suppliers I use, one for acrylics & one for canvases. Both produce very acceptable results nicely comparable to my original submissions.