It wasn't clear to me if Comet is doing something that was purposefully built in or trained in to let it do things on Amazon, or if it was built/trained to try to do things on any website.

From what the net tells me it is the latter. There is no special "work with Amazon" stuff.

If that's true I expect will lose when the actual trial takes place and when that is appealed. (The decision today is just about a preliminary injunction before they get to actually trying to decide the outcome of the case).

I expect the reasoning will be similar to that used in copyright cases when the question was if the user is the sole infringer or the tool maker can also be liable. There it came down to whether the tool has substantial non-infringing uses.

I'm sure Perplexity will have trouble showing that there are a large number of website owners that don't mind Comet helping people on those sites so unless something was specifically built into Comet for Amazon I expect that will be good enough.