I do not believe the Google Assistant has any ability to interact with WIndows at all, and from all I have read researching this for you, I would not use Google Assistant on PC but instead get a Google Mini or other device to set on my desk (and elsewhere in the house), which I have here alongside Amazon Echo and use each multiple times a day for whichever one does the task best. Basically I have Alexa control lights, TV's and devices, and Google for voice search, Calendar and alarms or reminders I also want on my phone.
I have never used Cortana since the times I've tried her she is not ready for prime time, at least not compared to OK Google and Alexa. I have read a few reports of Cortana working for some, but they are few and far between.
I hope this helps.