Unable to turn on ECO mode

I think the "ECO" selection you found in Settings is for whether the multi-information display ECO icon will be displayed: the one that shows above the hybrid-system indicator when you're not accelerating too hard.

As for the green ECO driving-mode indicator, it seems there are two possibilities to be distinguished: either (1) the button inputs are being recognized and you're in the driving mode you want, but the dash doesn't show it, or (2) the button inputs aren't being recognized and the mode isn't changing.

Are you confident you can tell the driving difference between the ECO, normal, and PWR modes? It's just a reshaping of the go-pedal-to-amount-of-go curve. PWR mode gives a bigger go response with the first small pedal input (at the cost of sort of flattening out with larger pedal inputs, to end up at the same place). ECO mode is less responsive at the first small pedal input (at the cost of exaggerated response at larger pedal inputs, again to end up at the same place). The same place all three modes end up at full pedal is the car's full power.

ECO also has effects on heating and air conditioning, which you might be able to notice. If the weather is hot and you have the A/C set to do a lot of cooling, you can probably perceive that it backs down a little in ECO mode.

If nothing is changing, the next question would be: does the ECU see you pressing the buttons? A scan tool that can display live data from the power management control ECU can show what I think are the states of the ECO button (called "ECO Mode" in Techstream) and of the PWR button (called "Pattern Switch" in Techstream). I've never paid attention to these myself, so I can't say whether they are direct switch readings (ON when you push, OFF when you let go) or readings of the current selected status (staying on after you select). Either way, they should give you an idea what's going on.

Does your EV switch have any effect, by the way?

You can also find an "ECO Switch" live-data item in the Air Conditioning ECU. Per the wiring diagram, that's where the wire from the ECO button actually goes. So the A/C ECU applies its ECO-mode power reductions directly, and the power management control ECU knows the setting (to adjust its go-pedal curve) by asking the A/C ECU.

The EV switch is wired directly to the power management control ECU. You can see the switch input in that data list under the Techstream name "EV SW2".

The PWR button is wired (hey, there are three buttons, so we need three different ways of doing it) to the ECM—even though in a Prius it's really another change to the go-pedal curve, which is calculated in the power management control ECU. So the power management control ECU knows the state of that button by asking the ECM.

As far as I'm seeing in an (incomplete, old downloaded) 2010 repair manual, there isn't any PID in the ECM showing you the PWR switch input state. Might be worth scrolling through all the items your scan tool shows anyway; it might exist but unmentioned in that old edition of the manual, or my eyes might have gone right past it.