Mediola could also be something to look into....
Island systems do not connect with each other. The communication between the systems is managed by the central unit or control. Processing times are always present, sometimes more, sometimes less. However, with current wireless protocols, these are already very low to hardly noticeable. You can always have problems with reception levels or signal strengths when radio is involved, depending on how congested the frequency band being used already is.
It gets complicated for you either way. Generally, the search term might be "smart home visualization" or "IoT gateway". But as I said: nothing will be easy, and it will tend to be a lot of tinkering if you want to do it yourself. There is no ready-made or out-of-the-box solution. I would worry less about speed and more about the situation where one of the many involved manufacturers changes something in their interfaces, then you are back to square one. But you always have that when you try to bring together so many toy solutions as best as possible.
The easiest way is probably to bring together everything that has "Alexa" or "Google" on it. That is almost a standard by now. For that, you then have Alexa and Google – but you have to want that as well.