'Independent Counsel', no. Independent Prosecutor, yes. Mueller could lead an investigation but had to hand off any prosecutions to the DOJ due to being an "inferior officer".
When the Biden DOJ kept going on about how independent the investigation was, how the Biden DOJ wasn't putting their hands on the scale to prosecute a political opponent, it meant that Jack Smith wasn't an inferior officer being supervised and directed. It was an independent office carrying out the prosecution, and independent offices need to be created by Congress as per the US Constitution.