Razer, when will thissstop?.. You need a video "wherein the mouse is connected to your pc via Bluetooth". So technically a video of a static screen. Big brain energy right here.
From the requested information only Windows version is relevant. This is not related to Synapse, since Synapse is irrelevant to Dynamic Lighting. Or rather its irrelevant to Dynamic Lighting seeing the device. RAM/GPU/CPU - completely irrelevant. What, do you want to tell me, that issue is because of bad RAM of too slow GPU or something? At best it could have been related to Bluetooth module, if you've asked for its model and driver version - that would have made sense.
But since you continue to insist to waste not only mine, but also your own time instead of just testing the issue, here's the video. It is the enormous 44 seconds long. It probably took me longer to upload to YouTube. The only real purpose it serves now is to show more people, how you are incapable of very basic testing, which is part of tech support job. And trust me, people will watch this: the other video of Synapse issue is the 3rd most viewed video on my channel, and I definitely did not promote it in any way.