China recovered its first reusable rocket and showed a new way to do it

I think there's a good chance that smoldering interstage is mostly just fuel dumping.

In every form of flight you want to ensure a certain margin for error, ideally they would have had more fuel than they needed to make sure they got their rocket into position. Conversely though, every drop of extra fuel they're carrying is extra weight, which puts extra strain on their landing system and their airframe, so as they approach the landing barge, they may be frantically dumping excess fuel. A fuel rich mixture tends to burn dark, especially with kerosene, as the smoke carries a lot of soot.

Personally, I think their high tension arresting cables are a brilliant solution for catching boosters, relatively simple and likely more reliable when compared to the chopsticks.

That said, chopsticks aren't just a catching system, they do catching and stacking. The chopsticks are designed to support a higher launch cadence, by not needing any additional infrastructure to handle stacking. For instance, with the chopsticks they can catch a booster, move it to the side, place it down, and be ready to catch a second stage within the hour. When they roll a new starship up to the launch pad, they don't need one of the largest cranes in the world to winch the second stage up, they can just use the tower.

Edit: Well Scott Manley released a video about this flight on YouTube and he doesn't think it's fuel dumping. Some Chinese reports have said that it was all part of the plan, dumping excess rcs fuel. But Manley says that's pretty unlikely, a more plausible explanation for that kind of thick black smoke would be burning hydraulic fluid (which makes some sense, because the hydraulic fluid for the grid-fin articulation would be housed up there). In general I'd trust his instincts over my own.

The catch is easier but with the chopsticks they can set the booster right back on the pad for refueling, theoretically

kinda, this is a novel method