You can’t get this specific BT tag to work with HASS. Once this tag disconnects it shuts off after a few minutes. You should get a NUT tag. Don’t pair them to your phone and they broadcast continuously without shutting off. The battery lasts for maybe 6 months, maybe even more. I haven’t really measured, but it’s definitely more than 3 months.
The other issue is that the Bluetooth tracker component is significantly slowing down Raspberry Pis so you should look at some of the other solutions discussed in the forum.