Your question would be much improved if you added one or more schematics giving us better insight into what your ideas are. Here's how to add a schematic..
In general, there are a couple of solutions that come to mind wrt "destabilizing the USB communication
":
Yes - you can add a separate DC supply to power the motor, but don't forget that the GND terminal of the servo's DC supply must be connected to the Pico's GND. Alternatively, you may be able to use a single supply (assuming it can support both loads), and isolate the Pico from the servo. As noted in the comments, some reviews of the 6221AMG servo suggest it can draw a substantial amount of current, and this Arduino Q&A suggests that a 2nd supply may be preferable - or even necessary - due to the 6221AMG servo having inconsistent supply voltage requirements.
If you think that the inductive kickback from the servo's dc motor is creating interference, a snubber circuit is typically used to tamp that down. However, you'll need to do some more research to apply this solution (i.e. I found no schematics online that would serve to guide wiring a snubber to the servo). If you can find a manufacturer's schematic, please add that to your question. There's a possibility the manufacturer has included a snubber or other suppression circuitry, but it's almost always a good idea to include one because it reduces stress on your switching components.
A few schematics add specificity to the words...
A dual-supply scheme:
simulate this circuit – Schematic created using CircuitLab
A single-supply scheme with power for Pico isolated from servo:
simulate this circuit
A snubber for limiting inductive kickback from a DC motor:
simulate this circuit
EDIT:
joan's comment (below) bears explanation; I'll make an effort to address it here:
It is true that servos and DC motors are not the same thing. If my answer implies this, I apologize for the confusion. Absent any data on the servo used, I took the fact that it used a dc power source as a clear indicator the servo contained a DC motor, and therefore presented an inductive load. Inductive loads produce "kickback" when the current is reduced (L*di/dt), and "snubbers" are routinely used to suppress that "kickback". Left un-suppressed, this "kickback" could potentially "destabiliz[e] the USB communication
". AFAIK, in-built motor drivers do not imply in-built snubbers, and so I suggested that one might be useful. It's often necessary to make assumptions in answering questions, but if these assumptions are misleading, any feedback that makes for a better answer will be appreciated.