A couple thoughts:
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You probably need to open the radio and solder components to the switch. You could 3d-print a structure to clamp onto the radio, with a solenoid and 3d-printed plunger to push the power switch, but that seems really kludgy (and difficult) to me. Soldering stuff inside the radio is probably better if you're okay with doing that.
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The controller is completely your choice, but I'm more comfortable with an Arduino vs a Raspberry Pi for most device-control. Hibernation-mode on the ESP-32 is 5 ?Amps (1 ?Amp = 1 millionth of an Amp, or 1,000th of a milliamp). But I don't think you care about the power-budget, so that's irrelevant. Used to be that RPi s were faster, but it seems the smallest ones are actually a little slower than an ESP-32, but you don't care about speed. Used to be that RPi s were bigger, but I just looked up size and you can get either device as just a surface-mount chip, or very tiny dev board now. Used to be that RPi didn't have wireless, but now it can. So it's a toss-up. I'm still going to give the nod to the ESP-32, however, since it's a simpler processor that is usually used for device-control, so has easy tools to do that specifically.
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However, you don't really need a controller. Use a BJT transistor / MOSFET / MESFET (or even the newer tiny relays), plus a capacitor, and you can make a simple circuit that will automatically connect the power button leads when power is restored. For a reboot (vs utility power-failure), you could put a simple and cheap internet-connected smart-switch on the mains plug, then turn it off and back on, with the circuit then "pushing the power button" for five seconds as soon as it gets power. This seems much less overkill than a RPi/ESP-32 and probable a lot more reliable.
SA5QED/David
Mr Wintle W1NTL