Yeah it’s a good question. For things like BTHome it (can be) built-in and automatic, but lots of devices will not advertise their battery level, but instead you need to connect to it and query the battery status. I think there’s a standard (GATT?) service for that, so I think it should be possible for an integration to offer that for any known / desired device supporting the spec-compliant way of doing it, but I don’t know of one. I think it is usually left up to the individual integration that supports a given device to handle this. That’s fine for a weather station or door sensor where you want some other integration to support features, but for beacons there’s not much other than Bermuda or some other passive listener that you would normally need.
I might be gradually talking myself into something here, so I’d better shut up.
So… as it stands, I don’t know of any “generic” way of getting BLE battery stats into HA other than via device-specific integrations.
If you want, feel free to jump into NRFConnect on your phone, “connect” to the device and see what services etc it offers. If you pop some screenshots in here I’m happy to look at what it’s doing/offering and have a bit of think about what options there might be.