What have I done? Video attached: Bad sound after oil change on ol' Blue

[Roostre]

That does sound like the fan intermittently hitting something. Can you grab the fan blades and wiggle them a little, after shutting the engine off, of course? Maybe your water pump bearing is going out, looks like there is a little drip of something on the crossmember under the fan.

[Chevy nutcase]

That's definitely the fan hitting something. Call me crazy but perhaps letting the clutch fly ripped one of the motor mounts just enough that now the fan is pinging that "shroud" that gm graciously put on there. Take the belt off and spin the fan to pin down what it's hitting