Capacitor interfering with servo

I have a a small project that includes a server and a servo. The sensor's manual says that I should use a 680uF capacitor, which I have set up.

The problem is that the capacitor is needed for the sensor and if I add in a servo to the same breadboard with the capacitor, the servo struggles to move. The servo works fine if I use it without a capacitor. What are my options to get the servo working?

Post a wiring diagram. Hand drawn is OK.
How is the servo powered?

You shouldn't be powering a servo and sensor from the same supply, that's bound to cause issues.

Here are pictures of the wiring

If I were to use two different power supplies, how would I do that and would it all work on the same arduino?

Share the grounds, the servo supply only to the servo so its not clobbering the supply for everything else.
Servos take 1A or more typically peak currents... Standard USB power is not sufficient for a servo, but
it looks like you are using external power. If you power the Arduino and sensor from USB, and the servo
from the external source, that ought to eliminate any issue with the servo.