Ok, I went ahead, and replaced the thing over the weekend, the whole procedure was simpler than I had expected. The supercharger removal was easy and didn't require any lifting of the engine or anything like that, maybe some bolts were hard to reach with the torque wrench when I assembled it back. That's the good part. I drove the car yesterday for some time, everything seemed fine, and left it sitting overnight.
But here is the bad part: I started the car this morning, but the rattle was still there, and got noticeably WORSE! It used to rattle for a split second just after the engine is started, today it rattled all the time while the starter was cranking up the engine, plus about a second after that. What could go wrong? I checked yesterday, did not notice any oil leaks, or any signs that something went wrong. When I bought a new tensioner, it didn't come with a central piece (the bolt that goes in the middle of the tensioner and pushes the spring), and the little plastic insert that goes inside of the spring. I just didn't know about those. I reused the both parts from the old tensioner. The insert looked like it is was worn by one side. Could that be a problem?

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2002 C230K