Yes, the Arduino SAMD boards are supported by the Arduino Keyboard and Mouse library.
Nano 33 IoT is a smaler alternative to MKR 1010.
But the MKR1010 or the Nano33 IoT doesn't support classic Bluetooth like the HC-05 module. The ArduinoBLE library and the NINA firmware support only BLE. But there is a simple way to replace the firmware with a basic Bluetooth sketch SerialToSerialBT and then use it from the SAMD.