Kai Morich's Android app Serial Bluetooth Terminal uses the Nordic_UART Service by default. There may be ways to change the app to use a custom service, but I have never tried to so.
You will need to write a program for the Nano33BLE which uses the Nordic UART Service UUIDs.
#define BLE_UART_SERVICE_UUID "6E400001-B5A3-F393-E0A9-E50E24DCCA9E"
#define BLE_CHARACTERISTIC_UUID_RX "6E400002-B5A3-F393-E0A9-E50E24DCCA9E"
#define BLE_CHARACTERISTIC_UUID_TX "6E400003-B5A3-F393-E0A9-E50E24DCCA9E"
There is a library which you can use with the Nano33BLE which implements that service. It is available through the library manager.
ArduinoHardwareBLESerial
There is an issue with this library and the Serial Bluetooth Terminal app, and without modification of the library the app fails to connect with the Error message
connection failed: no write characteristic(4/16)
To fix this error, go into the library .h file and see line 101
//line 101
BLECharacteristic receiveCharacteristic = BLECharacteristic("6E400002-B5A3-F393-E0A9-E50E24DCCA9E", BLEWriteWithoutResponse, BLE_ATTRIBUTE_MAX_VALUE_LENGTH);
Change it to this
BLECharacteristic receiveCharacteristic = BLECharacteristic("6E400002-B5A3-F393-E0A9-E50E24DCCA9E", BLEWrite, BLE_ATTRIBUTE_MAX_VALUE_LENGTH);
Make sure to save the changed file.
With this modification, the library example SerialPassthrough works with the Morich terminal app.