I have no idea how the FindMy BLE system works, but i strongly suspect that the cheaperst compatible "tag" you will find will be an iPhone. Might get a tad expensive to do this...
Assuming the newest ipod touches will work with this, $200 is the cheapest you could do this with in terms of using an iOS device (not that i'm suggesting this is a great option. As pointed out by the other second-level comments, you could just use tile or a real gps tracker without needing iOS).
The potential of low cost tags is in the first paragraph, and an overview of how the system would work is in the second. My takeaway is that you will be able to use something far cheaper than an iPhone.
