A while ago, my topside showed an OH error message and the GFCI tripped off. I turned it back on and although it hasn't tripped again, my spa won't power up. I checked through some things on the spa board and all seems fine, so I took a look at the breaker and discovered that the wires going into the box are fried and the posts are melted.

The breaker is a square D QO series 50 amp 240 volt. The only visible damage is the melting on the two hot wires going into the box. One fell right out when I touched it, so maybe they weren't seated properly and this caused the meltdown? I ordered a new breaker, but haven't picked it up yet.

Is it possible that this damaged the circuits on the hot tub as well? Is it ok to bypass the breaker temporarily just to test if the spa will power up?

Loose connections.

It happens all the time.
Be sure to trim them back until you get perfect copper. You may have to pull the cable in a bit to do it. Those things are a pita.