Not a direct answer, but I do use a Airthings Wave+, and the other day, I needed to replace the batteries. The Wave + worked just fine, before I replaced the batteries.
Now I cannot pull data from the device, through ESP BLE Gateway.
It did work stable, before the battery-replacement.
I have checked with my phone, by installing the Airthings app again. My phone does connect without problems. A firmware-update was also waiting, so I also tried that (2.2.0 firmware is the old one, as HA cannot talk with the device right now). I have removed the app from my phone, to secure it does not try and talk with the Airthings Wave +.
The output from my BLE gateway looks like this;
[12:53:57.969][D][esp32_ble_client:142]: [0] [40:79:XX:XX:XX:XX] Disconnect before connected, disconnect scheduled
[12:53:57.974][D][esp32_ble_client:354]: [0] [40:79:XX:XX:XX:XX] ESP_GATTC_DISCONNECT_EVT, reason 0x100
[12:53:57.975][D][bluetooth_proxy.connection:374]: [0] [40:79:XX:XX:XX:XX] Disconnect, reason=0x100
[12:53:57.979][D][esp32_ble_client:197]: [0] [40:79:XX:XX:XX:XX] ESP_GATTC_OPEN_EVT
[12:53:57.981][D][esp32_ble_client:291]: [0] [40:79:XX:XX:XX:XX] ESP_GATTC_OPEN_EVT in IDLE state (status=133), ignoring
[12:53:57.985][D][esp32_ble_tracker:135]: connecting: 0, discovered: 0, disconnecting: 0
[12:53:57.987][D][esp32_ble_tracker:861]: Setting coexistence preference to balanced.
[12:53:57.989][D][esp32_ble_tracker:214]: Starting scan, set scanner state to STARTING.
[12:53:58.282][I][bluetooth_proxy:056]: [0] [40:79:XX:XX:XX:XX] Connecting v3 without cache
[12:53:58.284][D][esp32_ble_tracker:135]: connecting: 0, discovered: 1, disconnecting: 0
[12:53:58.285][D][esp32_ble_tracker:813]: Stopping scan to make connection
[12:53:58.290][D][esp32_ble_tracker:821]: Promoting client to connect
[12:53:58.293][D][esp32_ble_tracker:857]: Setting coexistence to Bluetooth to make connection.
[12:53:58.294][I][esp32_ble_client:111]: [0] [40:79:XX:XX:XX:XX] 0x00 Connecting
[12:53:58.296][D][esp32_ble_client:209]: [0] [40:79:XX:XX:XX:XX] fast conn params
[12:53:58.308][D][esp32_ble_tracker:772]: Scan stop complete, set scanner state to IDLE.
[12:53:58.308][D][esp32_ble_tracker:135]: connecting: 1, discovered: 0, disconnecting: 0
[12:54:18.328][D][esp32_ble_client:354]: [0] [40:79:XX:XX:XX:XX] ESP_GATTC_DISCONNECT_EVT, reason 0x100
[12:54:18.328][D][bluetooth_proxy.connection:374]: [0] [40:79:XX:XX:XX:XX] Disconnect, reason=0x100
[12:54:18.328][D][esp32_ble_client:197]: [0] [40:79:XX:XX:XX:XX] ESP_GATTC_OPEN_EVT
[12:54:18.328][D][esp32_ble_client:291]: [0] [40:79:XX:XX:XX:XX] ESP_GATTC_OPEN_EVT in IDLE state (status=133), ignoring
[12:54:18.329][D][esp32_ble_tracker:135]: connecting: 0, discovered: 0, disconnecting: 0
[12:54:18.337][D][esp32_ble_tracker:861]: Setting coexistence preference to balanced.
[12:54:18.338][D][esp32_ble_tracker:214]: Starting scan, set scanner state to STARTING.
[12:54:18.585][I][bluetooth_proxy:056]: [0] [40:79:XX:XX:XX:XX] Connecting v3 without cache
[12:54:18.640][D][esp32_ble_tracker:135]: connecting: 0, discovered: 1, disconnecting: 0
[12:54:18.640][D][esp32_ble_tracker:813]: Stopping scan to make connection
[12:54:18.641][D][esp32_ble_tracker:821]: Promoting client to connect
[12:54:18.641][D][esp32_ble_tracker:857]: Setting coexistence to Bluetooth to make connection.
[12:54:18.641][I][esp32_ble_client:111]: [0] [40:79:XX:XX:XX:XX] 0x00 Connecting
[12:54:18.641][D][esp32_ble_client:209]: [0] [40:79:XX:XX:XX:XX] fast conn params
[12:54:18.641][D][esp32_ble_tracker:772]: Scan stop complete, set scanner state to IDLE.
[12:54:18.642][D][esp32_ble_tracker:135]: connecting: 1, discovered: 0, disconnecting: 0
I'm not really sure what to do now.
Remove the device in Home Assistant, and try again?
I'm not really sure what to do next, as I've tried what I can think off. Maybe the next step will be submitting a issue; GitHub - Airthings/airthings-ble: Library to control Airthings devices through BLE, primarily meant to be used in Home Assistant. · GitHub
But it must be something minor, I just need to adjust, or similar... However, I've not made any changes, since the battery-swap.
Update:
As I noticed it worked just fine if I usd ESPHome and the airthings_wave_plus platform, I decided to remove the Integration. After ESPHome was done compiling and data was showing up from that, well... Airthings showed up again as a discovered device. I added it, and wolla, things worked again. I don't get why. But, now it works again.