Yes — Bookmote works with Kobo Clara BW.
VerifiedPage-turn only — Home/Back/e-ink refresh don't work (Kobo's native reader only listens for page keys)
Part of Kobo (recent Bluetooth models): Clara 2E/BW/Colour, Libra 2/Colour, Sage, Elipsa, Elipsa 2E — expected to work (HID arrow keys supported); hardware verification still pending for models other than Clara BW
Source: Play Store review; r/eink report
Most e-readers put their Bluetooth radio to sleep after a period of inactivity to save battery. If page turns stop responding, tap your e-reader's screen to wake it — Bookmote reconnects automatically once the device is awake.
Bookmote has been confirmed to work with: Apple Books (iOS app), Kindle for iOS (iOS app), Google Play Books (iOS app), Adobe Acrobat (PDF) (iOS app), RIDI (iOS app), Kyobo eBook (iOS app), Millie (iOS app), yes24 (iOS app), Kindle for Android (Android app), Google Play Books (Android) (Android app), Adobe Acrobat (PDF, Android) (Android app), KOReader (Android app), Batcave (comic reader) (Android app).