Thanks for watching the video. I would have see what you're explaining. But if you have rusted off / "corroded off" ground wire, then it sounds like your water heater is older and into its end-of-life expectancy. (Average life expectancy on electric water heaters are 15 years). I would recommend contacting a licensed plumber and consider replacing the water heater.
I would have liked to seen the actual fix. So drilling a hole in the casing of the water heater and bonding the ground is good enough or should you run a ground to tank and hot and cold water lines?
Once the metal cover plate is attached to the top of the water heater, the ground wire now is now grounding the whole tank. Additional grounding can be done with conduit or Greenfield pipe for the wire that feeds the water heater when it is attached to the electric cover plate and the other end is attached to the breaker panel. Also, adding a jumper ground wire to the water pipes above the waterheater can be done. However, when plastic pipe or pex water pipes are used anywhere along the system, YOU LOSE your grounding.
Could be worse. Lol. When I started my apprenticeship last spring, one of the electrician that i was working along with, (ironically we were discussing the requirements with bonding the pipes together at an electric water heater) was telling me 15 yrs ago while we was on a service call the homeowner complained of receiving shocks while touching the faucets in the bathroom. Sometimes the homeowner would get shocked , other times no shock. The home in question was about 70 yrs old at the time and had knob and tube feeding the water heater, as well as many other f--- up's he would rather not tell me (guess so not to give me bad ideas??) and a wire burned off a thermostat and touched the metal jacket. How that home never caught fire is beyond belief.