Good afternoon. I’ve already replaced this once but the noise appears to be coming from the tensioner. Easiest to hear at idle.

 

I can only reply from my own experience but yeah - I had at one time replaced my belt tensioner with a less expensive one. Although I don't recall the brand, it seemed to begin to fail within 8months or so.
The noise in your video also sounds rather reminiscent/similar to a idler pulley going bad. I noticed the change in squeal/clatter when you were adding or releasing tension on the belt.
How many miles are on the belt?

 

Check the plastic bushings at either end of the hydraulic rod that is part of the tensioner. They dry out over time, crack and fall out. That allows the eyelet on one or both ends of the rod to rattle against the holding bolts. If that's your problem there is no need to replace the tensioner. A new hydraulic rod can be purchased separately (~$25). It's an easy fix through the passenger side fender well. Two bolts and you're done.

 

Thank you. The spring I place pressure on is for the tensioner pulley correct? This unit is nearly new. I have less than 3000 miles on it and it's the second one. I didn't realize there was an idler pulley as well. Would that be the same result after putting pressure on the spring to make the clatter disappear? The belts also are new. I tried to replace all the pulleys except the water pump when I replaced the supercharger pulley with a 15% reduction unit and new (correctly sized) belt.

 

That spring is part of the tensioner assembly. If the tensioner is new the rod attachments should be fine.

 

Here's a snip of the serpentine belt and tensioner diagram/routing


@cooper48 offers a good suggestion with respect to the plastic bushings and the rod wearing as a cost effective replacement option.
Had I known; I myself may have gone that route and tried the method of replacing the rod rather than dropping $200 on a genuine Mini replacement (not a bad decision mind you).
My replacement genuine Mini tensioner has lasted well over 35k with nary a rattle.

Although I am not a mechanic by occupation - In my case:
I have had 2wo idler pulleys go bad on me. The first time it had detonated into shrapnel leaving me stranded having to flatbed to a repair shop.
The second time; I was the wiser since my previous experience - I recognized the grinding rattle and high pitch that almost sounded like a baby supercharger whine.
I confirmed that the pulley was beginning to fail by pulling back the wheel liner and spritzing some soapy water on to the pulley bearings while the engine was running as a friend gently stepped on the pedal intermittently holding at about 3k rpms.
The noise went away. A $30 idler pulley and a 15% SC belt replacement has been doing well for the last 20k miles so far.

Not to suggest that your idler pulley is at fault.
but just a thought as to something to consider when further investigating/diagnosing the noise.