I played with a project like this as a kid in the 60's! It was from a book called 103 Simple Transistor Projects by Tom Kneitel (IIRC). I found the book in a dusty part of my bookshelf and photographed the circuit. Its sort of a crystal set that rectifies and filters what's available. The author says you can get 300 uA at 3v or 1 mA at .8v. I don't remember but this sounds about right, it wasn't much and I lived near a city. I used a very long wire antenna (100') and a ground stake.
Thinking today, I might make it kind of lower Q to get the whole AM band basically or perhaps build multiple receivers LC plus a diode tuned to several stations and or'ing them together.
Your other question about measuring power, you need a field strength meter or a spectrum analyzer. You could use a reciever if you get clever. Ask a ham operator for some help.
I've build a fair amount of remotely powered stuff mostly for Ornithologists. I would try solar first even if you think you're shaded etc. Find a location where there is some sun at some time in the day. Use an energy harvesting chip (LTC/Analog Devices make them). They will take a feeble output and charge a battery. A small gel cell lead acid or a NiMh battery would be best probably. You could also try a supercap but you'll need pretty low leakage. You could have a comparator that watches the battery/cap and sends a burst when it gets enough. I would just sort of be a relaxation oscillator that will do its best. You'd get more message when the weather was good and less otherwise. You might also consider other EH techniques like wind.
Another technique is just to use an oversized battery with good storage life and forget charging. Modern alkaline cells have shelf lives of many years especially when loaded very lightly. I've built audio players that play bird calls at sunrise or sunset for an hour or so. They use a 12v 35AHr lead acid (mini car battery) that lasts about a year of playing for an hour a day.
I googled RF Energy Harvesting and got this link.
https://www.eetimes.com/powering-the-future-wirelessly-with-rf-energy-harvesting/#:~:text=RF%20energy%20harvesting%20is%20the,current%20(DC)%20power%20source.Below is circuit from my childhood- post your results and enjoy!