BabyGeezer:
ehm... isn't that the basis of the scientific method ?
you don't know - but you guess* what it is, and then that guess is either validated or proven wrong, at which point you will then DO know (something).
- = educated one, conjecture or theory...
Close. The scientific method is more like: propose a theory, design experiments that can test it. Definitely not "just try something". Repeatability is part of this.
In your case, you concluded "not enough power due to the BT module". The simplest experiment to prove/disprove this would be to remove the BT module from the circuit, see if the jitter goes away. That's an experiment I don't see in your power supply tests. I expect it won't make a difference, if only because BT is designed to be low power, secondly because the power requirement of a BT (or NRF24) module is far less than that of a typical servo.
Your PCA9685 should be perfectly fine as it just provides the signal for the servo, not the power (unless you wire it totally wrong). If used with LEDs it can probably drive LEDs directly. An LED takes 10-20mA typically, a signal ideally no current, in reality maybe a few µA, should be <1mA. No problem there.
Pi filters work well. I'm using them mostly on the MCU side, to keep the noise of the motors out. That's when using a 12V circuit supplying power to a number of motors and projects. 12V supply, diode (Schottky for lower voltage drop but a 1N400x will do just fine), then Pi filter before the 12V-5V buck converter. The diode is to prevent back flow, really helps in my case even though I'm using 1.5 mm2 wires.