It’s worth speaking in terms of energy not just heat. Sunlight bouncing off a reflective curtain and going outside is one of their benefits.
An awning is a net benefit over a curtain alone, but there’s overlap in functionality so having a curtain reduces the net saving from adding an awning.
Curtains work poorly at keeping heat out, in large part because the temperature differential can be extreme if you let sunlight hit the curtain (that and air convection behind the curtain).
The alternative to awnings are shutters or, like you said, plants, but not curtains.
You can see curtains because photons are escaping out of the window. A white curtain reflects more sunlight outside than your room would. Similarly, a hot curtain really does emit more infrared radiation outside than your air conditioned room would. It’s not even just radiation, warming the window itself causes it to reject more heat via conduction and convection with outside air. Not all curtains are equally effective, but in full sun we can be talking a 30+ degree temperature difference between the room and a good curtain.
Shutters can effectively block sunlight, but they also emit IR radiation 24 hours a day based on their temperature. If it’s hot outside, thick reflective curtains really can save more energy across a given day than shutters though they also work better together at some point you might as wall just seal up the window.
I'm not sure I follow what you're saying. A blind outside is just like a curtain, except that to whatever extent it heated up it is heating up directly outside (via radiation or convection). A curtain that's hot in the insulated enveloppe is strictly worse, everything else being equal (color, etc.)
The radiation of the sun has to go somewhere. More of it will be reflected back by shutters, and whatever is absorbed can more readily be dissipated outside than inside.
An awning is a net benefit over a curtain alone, but there’s overlap in functionality so having a curtain reduces the net saving from adding an awning.