A bigger servo?
You need to measure the torque needed to turn the handle and then get a servo that has greater torque.
Torque is measured in Newton metres (or lbs feet). For example a force of 9.8 Newtons (1 Kg) acting at the end of a 1 metre lever is a torque of 1 Nm. It would be the same as 2Kg acting at a distance of 0.5 metres. Hanging a weight on the door handle and measuring the distance from the centre of rotation will give you an idea of the torque. Assume a substantial margin of error.
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