Colors more saturated in web posting than in PSD and on my computer?

What’s important here is what color space your image current has assigned to it. (Edit > Assign Profile) This is separate from the Working Color Settings.

If it was set to “Don’t Manag...” the image will be viewed according to the Working Space that you have set, in your case sRGB. This is pretty normal, and sRGB us “usually” the default online. However, if you export this file without embedding a profile, it will be considered “untagged” so wherever you upload or view it will assign whatever profile they want to it, which can change the look.

If it was set to “Working… sRGB” just make sure when you export the JPG that you embed that profile so the end viewer knows what it’s supposed to be. If you don’t embed, it will still also be considered untagged.

If it was set to something specific, like “AdobeRGB”, make sure that one is embedded as well. Agian, it would be considered untagged if not embedded.

If you’ve done everything correctly, wherever you are uploading it to is either not properly reading your embedded profile or ignoring it and doing something else.

Ironically, the situation that most people experience is the reverse: they complain the brighter colors in their image are displaying duller online, and this is usually because one is working in a wider gamut like AdobeRGB, failing to embed the profile, hence the colors are read in a different profile (usually sRGB which is a more limited gamut so the colors will be duller).

1 - Make sure the sRGB profile is embedded in the file. This is a separate checkbox in both Export and Save For Web. Photoshop Color Settings does not affect this.

2 - Use a web browser that supports color management and check that color management is working properly. Chrome and Edge both appear to be rather buggy here and it sometimes works, sometimes not. Firefox is much more stable and reliable.

Even so, many websites strip the color profile from images. Not much you can do about that.

As for image viewers, Windows Photos is fully color managed and will display identically to Photoshop. But a lot of other photo viewers are not.

The bottom line is that for web, all you can do is convert to sRGB and embed the profile. Done. That defines the colors unambiguously and ends your responsibility. If things are set up correctly on the receiving end, it will display correctly. If it’s not, there’s not much you can do.