Will that initiate actions like the voice thing does? I thought it just returned search results.

Google assistant on your phone can accept text input. If you're on a relatively recent version of Android you should be able to long-press the home button, then tap the keyboard icon in the popup. Works the same as a voice prompt

A lot of assistant functionality is just getting data from the internet, which search engines already know how to present and format in a useful way.

If you need to go to a specific spot in the house to write some text that turns on a light it seems easier to just walk to an actual light switch? For general automation then I think there are some visual block-based configurators to set up triggers for smart appliances otherwise.

Why do I need to go to a specific spot? I have devices that take text input on my body at all times, and I sit in front of one for most of the day.