I’m not sure if this meets your use case, but I’ve had moderate success with the circuit playground bluefruit from adafruit:
- device: Circuit Playground Bluefruit - Bluetooth Low Energy : ID 4333 : $24.95 : Adafruit Industries, Unique & fun DIY electronics and kits
- case: Adafruit Circuit Playground Express or Bluefruit Enclosure : ID 3915 : $4.95 : Adafruit Industries, Unique & fun DIY electronics and kits
It is 50mm diameter which is 10mm bigger than your requirement and only has a 3dof IMU onboard but I’ve had some successes with running tinyml models on it. But of note, it does have an nrf52840 chip which is the same as the Arduino nano 33 BLE sense and a built-in JST lithium polymer battery adaptor. The circuit playground are popular in hobby/costume wearable tech projects, so I highly recommend it if you need an alternative to the arduino nano 33 BLE sense.
p.s. I’m not sponsored by either Arduino or Adafruit (or anyone!)… just an enthusiast whose used their products 
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