This is the same tech that is in AirTags, but if you made your own beacon, you could have much control over power output.
Apple documentation: https://developer.apple.com/nearby-interaction/
Here's one chip - there are others though: https://www.qorvo.com/products/p/DWM1000
Forum discussion on ranging: https://forum.qorvo.com/t/dwm3000evb-max-range/11906/5
Away from a city, out in a forest, phones have access to GPS sats and that's about it - no additional location data from nearby "hot spot" routers, etc.
And GPS by itself (with no base station differential o post processing or other tricks) isn't that great down at the couple of metres range.
I myself would be looking more towards a cheap builders laser distance ruler or a piece of string with a loop about a middle stake hammered in the sample circle.
Back when I did this for a bit we were interested in insect and small things counting and used a section cut from a 44 gallon drum .. just drop that down and count everthing inside, then stand up, take X steps forward, drop and repeat.
KISS (Keep It Simple S...) works pretty well.
(As an aside, outside of a forest in a controlled environment there are photgrammetry tricks you can use if you can clamp the camera parameters and mount reference boards so that triangulation can be done from a snapped photo ... but it's over complicating things in a forest I suspect)
“another wireless communication technology called ultra-wideband, or UWB — specifically Apple’s UWB solution with the Nearby Interaction framework and Apple U1 chip-enabled devices, including AirTags. UWB provides precise location and distance ranging, much like the older iBeacon technology but more predictably and accurately. In fact, UWB RF ranging can detect distances as close as a few centimeters!”
I don’t know what range it provides, but it apparently can be used for fining your phone, so 10m seems not out of reach.
Or if you can limit it to newer iphones, I think their special UWB antenna lets them accurately sense direction and distance to an Airtag. Some newer Androids have this too but the ecosystem is immature compared to Apple's.
Edit: I think the pet industry also makes radio frequency pet trackers that don't operate off GPS or cell, just a tracking collar and a handset that tells you range and direction. Maybe they can wear one of those along with your app? It's probably easier / more accurate with the right hardware than trying to shoehorn it into an average phone...
It's possible that an electronic based system could be built, but it would require two transceivers that can measure phase differences of nanoseconds between transmitted and received signals. I'm not aware of any cheap off the shelf systems like that.
There may be better solutions out there, but you should also make sure that you know what the possibilities are with the old tried-and-true systems. Then you've got a baseline that you can use for comparison, and see how you can better that with other options.