Not sure what I'm supposed to be looking at in the second pic.
+1
That badge can just be riveted back on.
Trouble is, there's likely a washer on the inside that's come adrift.
And it needs a washer for the rivet to work against, it'll just fuxxor the carbon otherwise.
So the can has to come apart.
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I see you've done that already.
If it's the end cap that needs to be welded, I'd remove it from the carbon shroud first.