Please correct me if I’m misunderstanding anything here –
I think I understand that a hex value of #AE0000 is meaningless without knowing what colour space it refers to.
If I write that in CSS as a background colour, and view it in a browser what colour space will it refer to?
Will it refer to my monitor’s colour space? Will it use the sRGB colour space?
We dont know. The browser should act as if the image and color info was sRGB and convert it accordingly, alternatively if you have a image with a embedded a profile it should work on that. However there is no guarantee the browser does that. Some browsers do some do not (and what intent does it use?). Also, most systems aren’t calibrated or even capable of displaying sRGB so the entire thing is a bit complicated.
To put this simply: Assuming the system is using and converting sRGB to whatever is the best and only bet you can take. Since its the only option in town you will take it.