I think your best option at the moment is to use the 'OnChange Inputbox' from the App Store.
You need to be carefull with client refreshes in the triggered MF (from my experience you should not refresh the enclosing entity)
Unfortunately, the only option to do this would be a custom widget as this is not part of the platform. You can always request this in the idea forum, If creating a widget please be aware that every round trip to the server (microflow call) has some delay so triggering multiple subsequent requests based on every character added/removed might not be the wisest choice, you could work with a slight delay though.
What do you want to do with the 'typing trigger' ?
Maybe u can use the Input Reference Selector from the App store if you want to set a relation.