Knowing GE, I pretty much doubt that water caused this damage. Their live parts are well stood off and water would drip behind. Is the bottom of the tub rusty? As an example: The Pontiac Silverdome had hundreds of GE load centers, switches and panel boards. That was a cold, damp, leaky place. None of the GE equipment ever shorted due to water during the years that I worked there. (They also had a couple hundred FPE Stab-Lok. Those melted or burned as if on a schedule!)
Does your load center use THQL series GE breakers? If so, the fault isn't the bus bar. (See #4). There's no need to replace the bus or load center.
Do you have room to skip the melted spot on the bus? Perhaps a tandem ("Piggyback") breaker will free up a spot so you can forever ignore the burned lug. Snap in a closure over the now empty spot on the dead-front cover.
If You Replace The Bus:
Replacing the bus is a lot quicker than replacing the entire load center. The new tub will certainly be larger due to the newer gutter space requirements. If your shop is piped, the project then becomes rather lengthy.
Bus Replacement:
For a replacement bus, I suggest starting with Salinger.
https://salingerelectric.com/ or 248 585-8330.
They have lots of new and used equipment and are a family owned business with lots of nice (and knowledgeable) people. If in Michigan you happen to be in the Metro Detroit area, the main location is on the north side of 15 Mile east of 75 in Troy. (They also ship items.) If you go there, ask for a tour. It's a fun place to explore!
They also have a store in Romeo off 33, between Van Dyke Freeway and Romeo Plank and one in Farmington Hills somewhere. I've not been to those two, but the one in Troy is loaded with treasures.
Plan B:
At the web site
https://electricaladvertiser.com/ click on the On Line Publications tab at the top. This will bring up copies of the mailed magazine. Inside you will find lots and lots of used equipment sellers. One surely will have the bus that you seek.
Hope This Is Helpful!
Paul