Well, regarding the phone thing, modern phones don’t have removable batteries, but it’s very unlikely that the cops have a way to access the camera and microphone even when the phone is on. Cops have a notoriously difficult time just unlocking a phone that’s in their possession. The FBI/CIA etc might be another story. Who knows what active exploits they’re using.
But if your phone is powered off, it won’t be sending or receiving any data, both of which require power and create EM signals that can be detected. Unless your phone advertises some sort of remote wake feature, once it’s off, it’s off. It is doing nothing but tracking the time (RTC is always on in all modern tech with any sort of battery).
Cops can, however, triangulate your location to within a block or two using your phone’s cell tower pings. Those happen as long as your phone isn’t in Airplane mode. It takes a while (like, an hour or two), and the phone company has to do it for them, but that’s often how they find missing people.
Edit: recent iPhones DO have a sort of remote on function, btw. It’s not cellular, but some propriety thing based on MagSafe, so it requires a machine to be within a few inches of the phone. Basically it uses the same circuitry as the wireless charging does.
http://nymph.io/
This project technically started in 2009, as part of another project called Dandelion (which then was renamed to Pines), then around 2014 I pulled it out into its own project, Nymph. I worked on it on and off, until 2021, when I rewrote it for Node.js as Nymph.js.
It now runs my email service, https://port87.com/
Here's the oldest code I can find on GitHub from July 7, 2009:
https://github.com/sciactive/pines-components/blob/144ce877e1ec9af7fa34c8eb8b11aeb7ae0efb5e/com_entity/common.php
And here's the first version as its own project from Sep 8, 2014:
https://github.com/sciactive/nymph/tree/fdf5f770da7e5acc6938debbaeb8c09cfd080e15/src