Are you comfortable with flashing microcontrollers? https://esphome.io/components/bluetooth_proxy.html might be a solution to your BLE beacon idea. buy any esp32 board for like 5$, put it somewhere in your living room or wherever makes sense and have it proxy BLE scans to HomeAssistant.
If you really just want to know if the kid (or better, the ble tag) is at home, then no - I’d probably use any other ble beacon (iBeacons are cheap on Ali)
Afaik, Tile tags work somewhat like AirTags and are trackable wherever they are. If you want/need more precise location information then I’d stick to Tile.