Welcome to the forums. You're talking to other customers here.
Short story: Don't worry about this. Unplug your old router. Plug in your new router. Done.
Long story: Verizon used to limit residential accounts to one IP address at a time. This meant it had to be released when changing routers. There were a variety of techniques to do this, as you've found all over the internet. However, most people couldn't figure this out and would contact Verizon support to have them release the lease. Verizon eventually figured out this was a waste of everyone's time. They updated their systems to allow two IP addresses to be allocated at a time, thus solving making router switches easy and painless.
Note that while they will allocate two IP address at a time, only one is allowed access to the internet. Thus, you can't plug two routers into one ONT and have both work. Only one router at a tme should be plugged into an ONT. But you don't have to jump through any hoops to release/renew IP address.
Like many things on the internet, people don't keep their old articles up to date with current practices.
One more note; if you have Verizon set-top-boxes, you should know that depending on model they may not work well with a non-Verizon router. If you don't have Verizon boxes, then have fun!
