post processing - How do monitor and image editing software color profiles interact?

I've Googled, I've Bing-ed, I've even DuckDuckGo-ed, but I can't figure this out.

Here it is:

My monitor has its own color profile, currently "eyeball" calibrated but soon to be really calibrated.

However, each of my imaging editing programs, specifically RawTherapee and Affinity Photo, have color management settings within which one is supposed to set a (or keep the preset) "default" color profile. I note that in both, I can choose the monitor's profile from a drop-down list. However, the preset color profiles in the image editing programs are sRGB IEC61966 ones. I note too that if I'm not mistaken, they both "keep" the profile embedded in the image by the camera or assign a profile if the photo does not have one (the case for raws, no?).

To round out the information, my monitor is a pretty run of the mill Dell (IPS just the same) that covers the sRGB gamut but not Adobe or other wide gamuts. Because of this limitation, I also have my camera set to sRGB.

But my question is how do the color profiles of the editing programs interact with the "calibrated" color profile of the monitor? If the programs are--I don't know--assuming(?) a standard sRGB, how does my calibrated monitor come into play? Or is it the other way around: If my calibrated monitor has control, what difference does the editing program's color profile make? Does one "override" the other??

I hope that all makes sense! The problem of course being that I'm asking about something that doesn't make sense for me, so...

Anyhoo, thanks in advance for any clarifications that you can share with me!

EDIT:

So just a quick thanks again to all those who have responded, with a special shoutout to LightBender for his great follow-up to my questions. But it's the synthesis of all the contributions that has helped clear up this point for me.

The big take home being that the monitor profile doesn't really "interact" with the image editing software; its role is more so corrective, so that the colors on the screen are as true as possible to the rgb values mapped in the color space (sRGB in my case).

And especially, you don't use the monitor profile as a working space in the editing software!

If I can, I would add one follow-up question: Do I understand correctly that my camera assigns a color space to jpegs, but not to raws?

Again, thanks to all (and in advance for this last question)!