No, blowing up the Death Star won't collapse Galactic Civilization.

What part of "it's a galactic civilization" did you miss?

1. The Republic/Empire is a robust Kardashev level II civilization, and not a young one. It's got a LOT of civilized worlds, and is clearly heading for KIII classification. Blowing up a whole planet didn't kick off a depression. Analyzing the resources of a civilization like that using assumptions based on our civilization is like Pliny the Younger looking at the possibility of building an aircraft carrier based on the resources of a slave-based economy and deciding that sinking a single vessel would collapse the world's economy.

2. The Death Star is not productive infrastructure. It's sunk costs. Any economic impact it has is in the past. If maintaining the production lines for the Death Star have a positive impact on the economy, then blowing it up to keep the lines flowing as you build another one is probably the best thing you can do. Of course those same production lines can be used for building, I don't know, modern housing for Jakku scavengers instead. Point is, there's no benefit to the Galactic economy from the continued existence of the Death Star.

3. They make a big deal about the amount of steel involved. That amount of steel is basically lying around in nickel-iron asteroids for the taking in any "dirty" system with a lot of small body matter. That whole part of the paper is like Pliny calculating how many slaves would be needed to dig up the iron ore for the aircraft carrier I mentioned two paragraphs back.