Hello,
By 'extension' do you mean the kernel extension?
If yes, and you were following
this article - then please notice that it does mention that the steps described in the article do not apply to DisplayLink Manager 1.x on Big Sur or Monterey. With DisplayLink Manager v1.x there is no kernel extension to be aproved.
It only applies to legacy software (aka. KEXT drivers) versions 2.2 to 5.2.6.
You will not see any DisplayLink extension with the new drivers.
Best regards.