Most products I see are compatible with Google Home and Alexa. Does this automatically mean they are compatible with openHAB?
Not for Google Home. openHAB doesn’t access devices through Google Assistant, so they have to have bindings or some other way to connect.
The Amazon Echo Control binding lets you control devices through Alexa, but I haven’t personally used this feature and I don’t know what its limitations are.
Saying this, I wouldn’t buy any devices on the theory that they’ll work with openHAB through Alexa. There are lots that we know do work with openHAB, and in many cases you’ll benefit from local control with no need for Internet access.