In my case, I had the issue not only with new paragraphs but even old ones as long as they use CKEditor5. I've looked into the ck-reset_all class who apply the background: transparent on the Linkit widget, and so despite the presence of the ck-reset_all-excluded class. And I realize that CKEditor reset class actually exclude everything below the exclusion class but not to the widget div itself (.ck-reset_all :not(.ck-reset_all-excluded *)). So the patch suggested by carma03 did not worked for me.
I came around with this by moving the background-color property to the linkit-result-line class to avoid this behaviour.