A quick update on what I have seen in home assistant. As noted, if you use the current switch position values then you will get nearly instant feedback, and I can confirm using the current switch position in a home assistant automation the lights began transitioning from on or off nearly instantly. However as also noted this approach is far from reliable as a good portion of button presses are completely missed.
The info I wanted to add is that I have some of the new Ikea Bilresa 2 button switches, these switches can detect singe, multi press and long press just like the Inovelli white series switches, (the automation I use to detect the button presses is the same between the Bilresa and the Inovelli switches) however I find that the Bilresa switches are much faster than my Inovelli switches and the Bilresa switches are battery powered!