Advice needed for first project

Hi All,
Let me start by apologizing if my question has already been posted. I am completely new to programming, coding and small electronics, but I figured if an 8yr old can build a robot I guess I can as well, so please be patient with me.
Recently, I saw an RF tracking device that is no longer available for purchase that I would like to try and recreate as my first Arduino project. The original device was used as a pet leash and pet finder that I would like to repurpose the detection feature of the equipment for other uses.
In many ways what I am trying to achieve can be classified as basic proximity detection and yes, there are many proximity detection options out there however, I was not able to find any that seemed to check all my boxes. In my search all I seem to find were devices that alarmed when something came into a particular zone or an object got too close to the transponder. Likewise, just about all of them worked via Bluetooth or needed a mobile device to complete the communication loop. To the contrary, I want a standalone system (transmitter/receiver only) where the receiver tag begins to buzz when it is taken outside of a preset or programed boundary limit.
My goal is to find the correct module(s) and buzzer that would allow me to program the pieces to search for one another and when one of them is believed to be outside of the programmed boundary limit the buzzer sounds until it is back inside of the parameter. I guess I am most confused with all the options available and I am unsure of the best place to start. Can someone please offer some suggestions about modules and technology options i may need to consider for this project? A video of the original product can be viewed here. Thanks in advance.

That looks like a BLE (Bluetooth Low Energy) technology. The tracking device is paired with a BLE receiver in the keyfob. When you get further tan the BLE range, it loses connection ad alarms. I am no BLE expert, but I recall that you can set the power level in Bluetooth, giving you a variable range.

I agree with @SteveMann, BT low energy is your best bet, but it depends on the range you require. BT could certainly be used to give you an alert when something moves more than, say, 5m away. If you need a greater range (more than 10m or so) you'd need a different wireless technology (I'd search for "low power 433mhz" ).
Tile uses BT and performs similar functions to that in your demo video.

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