Flow doesn't support ChromeOS, which is what my work laptop is (and I didn't get to choose it). Without ChromeOS support this functionality is useless to me.

If ChromeOS cannot be supported then I should be able to map a button/movement of my choosing on my mouse (MX Master 3) to cycle through paired desktops. Or even better, let the desktop selector on my keyboard (MX Keys) also control my mouse. I bought them with the idea that they'd be paired together, but it seems they don't actually interact with each other in anyway.

Even if it only required a single Windows/Mac computer that would be fine. The keyboard/mouse could always be anchored to a computer that runs LogiOptions in order to control both K&M using a single button (like the pre-existing one on the keyboard) and it could send a signal to the mouse to cycle desktops based on the keyboard's input. (or if you're really brave then find a way to have each device talk directly to each other securely).