Pat Kirwan said he heard Carr didn’t want to do Saints contract restructure

It's 5 different reporters so it's at least 4 or 5 sources and probably more.
No, it's not. That's a speculative assumption.

It looks and reads a lot more like an echo chamber of them all repeating what the other "reporter" is saying.

When they are saying "I'm hearing" they are talking about their colleagues. Notice they don't say "sources told me." It's always "I'm hearing" or "sources are saying." They don't want to be left out of the story, because they don't want to lose viewers which would cost them money.

Even if each of them has a source, all of them could be relying on the same person as their source.

Beyond that, none of the 5 have cited or mentioned the other reports.
Of course they haven't. That's not how it works. They all want to seem like they have their own sources. Their viewership depends on it. You wouldn't value what Underhill and Triplett say if you didn't think they have credible sources.

I really don't understand why people so badly want to think Carr wants to be here.
I really don't understand why so many more people so badly want Carr to not want to be here. Actually I do, it's because it fits their perspectives and opinions of Carr. It's textbook confirmation bias.

And to be clear, I don't blame him for not wanting to be here.
You choose to believe that Carr doesn't want to be here based on these very flimsy rumors, because you don't like that he's the Saints' QB. That's exactly how confirmation bias works.

And by the way, rumors are often repeated by multiple people who all say "I heard that..." That's exactly what's happening here.

Not a single one of these "journalists" have said that they reached out to Carr for comment. That's one of many reasons that they are not engaging in actual journalism. They are just fishing for clicks so they can pay their rents or mortgages. I don't fault them for that, I just see it for what it is.