Bug 1543185 landed a first version of dispatchMouseEvent where button is automatically set to "left" when no button argument is passed or if it is set to "none".
At first sight it doesn't look like chromium does the same as mousedown/up/click events aren't fired in these cases.
So it isn't clear what should be done in these two cases, but right now Firefox will fire left click/down/up events.

Given the CDP documentation the default for the button is none:
https://chromedevtools.github.io/devtools-protocol/tot/Input/#method-dispatchMouseEvent

Best would be to check with a CDP client in how Chrome behaves here, and apply the same logic to our implementation.

Our WebDriver BiDi implementation meanwhile supports the input.performActions command for key and mouse events. As such we won't spent time on CDP issues.