Elements 2020 is only compatible with ACR 12.0 and has never supported version 12.1.
You can't update ACR manually in Elements, only from the menu Help >> Update.
The ACR version of Elements does not offer the same tools as the full Photoshop options. Apart from the support of new cameras, the 12.1 version for Elements will be exactly what you have now.
You are mentioning Bridge: Bridge itself does not link to the ACR module unless you have a "Berechtigtes Produkt ", that is either Elements or Photoshop. Depending of which sofware you have in your computer, it will show the right version. If you have used Photoshop before (even a temporary trial vesion) you have probably used the full Photoshop 12.1 ACR version. You can download and install the 12.1 version for Photoshop, it will not be recognized by Elements 2020.