Yes, indeed! What worked for me in the end, was to first understand state observers (e.g. Luenberger observers) and then consider a Kalman filter as an optimal

Yes, indeed! What worked for me in the end, was to first understand state observers (e.g. Luenberger observers) and then consider a Kalman filter as an optimal observer, where the observer gain is the steady-state Kalman gain. The whole duality between state-feedback design and observer design -- and LQR and Kalman filters. Then it made sense :-)