Similar issue. It seemed to happen with me when I installed either 16.3 or 16.3.1 on my iPhone. Not only did my CarPlay screen lose my garage door button Siri Suggestion (which had worked perfectly until then), I also now can’t open it by talking to Siri on CarPlay. If I do, it tells me I’ll “need to unlock my iPhone first, but I don’t recommend doing that while you’re driving.” The same command to my Apple Watch works fine. Also, I can tell Siri to close the garage door in CarPlay, and that works as well.
I’m really disappointed in losing the button on my CarPlay dash because that was the easiest, fastest, and most reliable way for me to open the garage door from the car.