Servo responds to servo tester, not to microcontroller. Signals look the same
This may be related to the output pin settings done by the .write() routine. Please try using a 1K pull-down resistor, it it doesn't work then remove it and use it  pull-up resistor. this will balance the effect of any internal week pull-up/pull-down resistor that may be set by the routine. When you are measuring the signal with your scope the internal resistance of the probe is acting as a pull-down.
Most servos will also release the power to the internal motor if the signal in not preset for 10 pulses in a row. This is used to save power.