What do mean IOS Bluetooth disconnection status codes?

Additional logs:

Code Block C
Feb 17 11:54:06 bluetoothd[82] <Notice>:  _GATT_LE_ConnectCompleteCB notification from lmHandle 0x00000040 with status OI_OK
Feb 17 11:54:07 bluetoothd[82] <Notice>:  _GATT_LE_DisconnectedCB on handle 0x000000010A5053A0 with reason  STATUS 762
Feb 17 11:54:07 bluetoothd[82] <Notice>:  _GATT_LE_ConnectCompleteCB notification from lmHandle 0x00000040 with status OI_OK
Feb 17 11:54:07 bluetoothd[82] <Notice>:  _GATT_LE_DisconnectedCB on handle 0x0000000105F05C40 with reason  STATUS 762
Feb 17 11:54:07 bluetoothd[82] <Notice>:  _GATT_LE_ConnectCompleteCB notification from lmHandle 0x00000040 with status OI_OK
Feb 17 11:54:13 bluetoothd[82] <Notice>:  _GATT_LE_DisconnectedCB on handle 0x000000010A5053A0 with reason  STATUS 722
Feb 17 11:54:14 bluetoothd[82] <Notice>:  _GATT_LE_ConnectCompleteCB notification from lmHandle 0x00000040 with status OI_OK
Feb 17 11:54:31 bluetoothd[82] <Notice>:  _GATT_LE_DisconnectedCB on handle 0x000000010A5053A0 with reason  STATUS 708
Feb 17 11:54:31 bluetoothd[82] <Notice>:  _GATT_LE_DisconnectedCB on handle 0x000000010A5053A0 with reason  STATUS 708
Feb 17 11:54:31 ring[387] <Notice>: [BLEAsset] didDisconnect(error:) <BLEAsset 0x000000028210dc20 { peripheral=<CBPeripheral: 0x28222aee0, identifier = 943990CB-0CB2-683A-A570-18AF87501036, name = my_name, state = disconnected> version=121 }> Optional(Error Domain=CBErrorDomain Code=6 "The connection has timed out unexpectedly." UserInfo={NSLocalizedDescription=The connection has timed out unexpectedly.})
...
Feb 17 04:37:35 bluetoothd[82] <Notice>:  _GATT_LE_DisconnectedCB on handle 0x000000010F405760 with reason  STATUS 719
Feb 17 04:37:35 ring[434] <Notice>: [BLEAsset] didDisconnect(error:) <BLEAsset 0x000000028215e010 { peripheral=<CBPeripheral: 0x28225f520, identifier = 7D9AF1C1-B7D5-2AF8-3101-906AB59B1CC5, name = my_name, state = disconnected> version=121 }> Optional(Error Domain=CBErrorDomain Code=7 "The specified device has disconnected from us." UserInfo={NSLocalizedDescription=The specified device has disconnected from us.})
Feb 17 04:37:41 bluetoothd[82] <Notice>:  _GATT_LE_ConnectCompleteCB notification from lmHandle 0x00000040 with status OI_OK
Feb 17 04:37:41 bluetoothd[82] <Notice>:  _GATT_LE_DisconnectedCB on handle 0x000000010F405740 with reason  STATUS 762
Feb 17 04:37:41 bluetoothd[82] <Notice>:  _GATT_LE_ConnectCompleteCB notification from lmHandle 0x00000040 with status OI_OK
Feb 17 04:37:41 bluetoothd[82] <Notice>:  _GATT_LE_DisconnectedCB on handle 0x000000010F405760 with reason  STATUS 762
Feb 17 04:37:42 bluetoothd[82] <Notice>:  _GATT_LE_ConnectCompleteCB notification from lmHandle 0x00000040 with status OI_OK
Feb 17 04:37:42 bluetoothd[82] <Notice>:  _GATT_LE_DisconnectedCB on handle 0x000000010F605220 with reason  STATUS 762
Feb 17 04:37:44 bluetoothd[82] <Notice>:  _GATT_LE_ConnectCompleteCB notification from lmHandle 0x00000040 with status OI_OK
Feb 17 04:37:55 bluetoothd[82] <Notice>:  _GATT_LE_DisconnectedCB on handle 0x000000010F7042B0 with reason  STATUS 708

These status codes are based on the Open Interface North America Bluetooth project. We cannot provide a preferred link to find this information, but doing a search for Open Interface North America status codes should yield useful results.

Specifically to your question, Status 708 indicates a connection timeout. Status 719 means the remote side has closed the connection.

You can see that these explanations of the status codes are also clearly printed in the logs you provided as CoreBluetooth errors.