I used an old Motorola phone for this, and yes, if it dies it won’t turn back on again until the power button is pressed. I Googled around and there’s a way to disable this behavior though, through an ADB command. The bad part is that it supposedly might get stuck in a boot loop – it tries to boot but there’s not enough battery yet, so it dies and keeps trying to boot. Over and over.

I made a second Tasker automation, so it shuts down with less than 15 percent battery. It might still get stuck in a boot loop, but eventually the solar panel will quickly charge it above 15% so that it won’t be for very long.

You can virtually power down a phone in Tasker without turning it off by shutting down all antennas and downclocking the CPU and GPU, disabling background tasks etc.

Most android phones have a feature that lets you set a time at which the phone should turn itself on at a certain time. I used this as a last resort in a project with similar requirements, but I don't remember if we ever ended up testing if it worked after fully draining the battery.

Interesting. The "power on when charging" thing appears to be a flag you can set, but not all brands support it.

When the phone is "off" but showing the charging animation, it's actually booted and the animation is a program it's running. There used to be a hack, I don't know if it works on modern Android, where you'd essentially edit the init scripts and tell it that the charging animation task should be the rest of the boot process, or your specific app of interest.

That's interesting. But the charging animation appears near instantly, while my phone takes a minute or two to start?