@DannyCoolBeans I looked up the part number for the mechanical tensioner and found it to be 11 31 8 544 896
For the installation, I will consult my shop manual (on DVD) once I get around to it, hopefully sometime over the next couple of weeks. The most challenging part looks to be the removal of all the plastic. There's also a video on Youtube on how to install a mechanical tensioner that I watched recently, in Italian I believe.
@Greg goes wild The first time the tensioner went bad, early 2018, the BMW dealer replaced it with another mechanical one. I doubt they would warrant that installation, now almost 4 years later.
I have no intention of going back to a BMW dealer unless I have no other option. I can do most mechanical things myself, having done all repairs and maintenance, including full engine rebuilds, on all my vehicles since around 2012. I only took the scooter to the dealer as it was still under warranty in 2018, and for the brake recall (I can't do recalls myself) and both times the dealers disappointed somewhat.