Delay for launching commands with Google Assistant

I use the Nabu Casa cloud integration to bridge between HA and Google Assistant.

A request such as “weather forecast for Shanghai” is instantaneous (I am in France and choose something that is not cached).

The request “close parent shutters” takes about 5+ seconds to start.

I think it was way faster when I was using the DIY integration (very well documented BTW).

I have the same delay when using the Home app so this is not voice processing or interpreting that takes time.

Did anyone has this problem and found a fix?