I went down that rabbit hole recently. First, I measured the id of that hole and got ~ 24mm. Ebay sells an 8-pack of white plastic 24mm hole plugs:
https://www.ebay.com/itm/281458643614 At $6.75 with free shipping, they seemed worth a try, and did fit pretty well. (I have 6 left over if anyone local needs a pair - at $.84 apiece, they are hardly worth shipping!)
If you want to use the BMW part, it's not the 51 41 1 869 871; that goes in the interior door panel and covers the hole that accesses the electric window motor coupler. Removing that plug allows you to turn the coupler manually when the motor jams.
The 41 51 6 754 244 looks more promising in its photo on the Walloth & Nesch site, but they show it as out of stock:
https://www.wallothnesch.com/en/catalogsearch/result/?q=41+51+6+754+244