Rekor will pick up the car because it is analyzing the video stream.
Plate Recognizer will attempt to read a plate for any image sent to it, whether a plate is there or not, and BI only sends one image per "event", so if the motion detection isn't set up correctly for your field of view to have the plate in view, then it will come back empty.
You have a tight field of view with a less than ideal angle, so I suspect that when BI detects motion and takes the image, the vehicle is out of view.
You first need to get BI to consistently show in the alerts the backend of the vehicle before you start messing with Plate Recognizer or you will blow thru the 2500 images per month.
So turn off LPR stuff (Rekor is fine to keep going since that is outside of BI) and then what do your alert thumbnails look like? Are they mostly blank or are you getting the plate in the image?