Some people used to use them to prevent glitching. Given the short wires - ideal length is super short.

it's a capacitor. I want to say it capacitates, and when dipped in flux you can go hella fast.

it's just acting as a "glitch buster" or something to that effect on your ESC internal battery eliminator circuit. It can also act like a filter, but being that big I'm guessing it's an attempt at solving receiver brown outs.

Be careful with those glitch busters, I would only use them as a last resort as they can potentially mask other problems that should be addressed first.

Brown outs can happen if you have not properly set the end points on the servo to where if it overloads the limit points, then you can get a brown out.
Some brands of servos (i.e. Savox) tend to be very inefficient and pull significantly more current which can overload the BEC and cause a brown out.
I have seen cases where a high flow motor cooling fan overloaded the BEC causing a brown out.

Consider the BEC on your ESC, I used to run a HobbyWing Justock which comes with a 2A BEC and a Savox 1258 servo, everything worked fine for over a year running several brands of ROAR approved 13.5T motors in my wheeler. Then I upgraded to a Trinity Punisher which is an Outlaw motor, then I started getting brownouts... I chose to upgrade my ESC to a ProStock with a 3A BEC and then my brownouts went away, chances are the glitch buster would've solved the issue but there were some other features that I wanted with the higher quality ESC anyway

are you sure it just isn't in blinky mode which is required for stock racing?

you can down load the Tekin manual from there website.. for free..

troubleshooting about the blinking LED's included...

also call them for help..

and take that average electrolytic capacitor off and pitch it.. my opinion...
to large for a noise filter.. to small for a brown-out buffer.

I have a similar situation