Pasting to web/programs desaturate colors dramatically

You need to post screenshots. It's impossible to say anything without seeing it.

Exactly what is your procedure here? Please explain how you copy, how you paste, and most importantly where and in what application you paste it.

Do these files have an embedded profile at all? Remember, this is not dependent on your working space or color settings. You check the embedded profile here:

The working RGB (as set in Color Settings) is just a default for new files. An already embedded profile will override that. If these files are coming from Lightroom, they will be ProPhoto, not sRGB.

But this sounds like cameron5 is making screenshots:

"It's not an issue of saving and uploading. That works just fine and doesn't change the saturation at all. Rather just directly copying from the canvas to wherever."

RGB numbers lifted off the screen have already been converted to monitor RGB, they are no longer in the original color space. So to represent this correctly outside Photoshop you need two steps:

First you assign your monitor profile.

Then you convert to sRGB.

I was going to suggest you check that you are copying from a file with a color profile of sRGB but it sounds like you are already doing that.

Are you using 8 bit files (Menu > Image > Mode)?