Yes. The only think "unsafe" (more like unhealthy for the battery) is to heavy use the phone while charging due to generated heat. BT uses very little battery, so it's totally fine.
Here's what I do with my TWS earbuds and TWS adapters (like FiiO UTWS3/5) or really Bluetooth/wireless/rechargeable/etc. stuff in general: I try to only charge it when it has no battery or will have no battery soon. And then I don't touch it at all while its charging.
marcelocampiglia t1_jc6js0u wrote
Yes, it is safe.