That is interesting. Is your dess key just the key part only? No lanyard or tether connected to it? When you take a video tomorrow, can you attach a picture of your key? If you only have just the key, without a tether, as seen in the attached pictures, then that is your problem. Typically people connect the emergency lanyard tether, that connects to the boat's engine kill switch, directly to their key. I personally do since I'm on a boat, not a jet ski, and not really able to do anything that could throw me off or out of the bucket seat. But again, if that lanyard isn't connected to the boat's kill switch, the engines will not turn on, possibly giving you that original 1 beep. And if that is the case, then you will not hear much of an attempt to start the engines.
According to your first post, with hearing 1 long beep, if you can confirm, then that indicates your shifter lever is not in he neutral position, as well as the tether not attached to the kill switch. If the levers are in the right position and tether is connected, can you also include in your video, all the beeps made, along with a clear view of your gauge cluster display on startup, as well as your throttle and shifter levers?
According to the owners manual for beep codes, which I am attaching a picture of, go through and see what your beeps mean or upload your video and I can help you if need be. At this point, id would turn the key all the way which allows the boat to perform the self check. When this happens, you should see the gauge cluster light up and the needles for the tachometer sweeping up to 10K RPM and back down, with the lights going away after the needles come back to 0. Then look at your voltage gauge and write down what it says. If it is 12V, then battery is fine, as you said, and connected properly. At this point, still wouldn't suggest firing up the engines just yet. Take the key out and power down the boat, using the battery switch. After doing that, check your fuses around the boat and see if anything is blown.
But do upload the video you take and I, as well as others, can review it and see if we can provide any additional help.