If you're in a country that has the Hubitat Skill for Alexa available, then you need that, and you need to install the Amazon Echo Skill App on Hubitat.
If you're in a country that does not support the Hubitat Skill for Alexa, then you need the Amazon Echo app on Hubitat. The naming IS very confusing, I know.
For Google Home, you need to add the Google Home app on Hubitat and in the Google Home app, you need to go to Home Control > Assistant > Manage > Accounts and search for Hubitat. Again, confusing names make this a bit confusing to navigate the first time.
The Chromecast Integration (beta) app on Hubitat is for TTS and playing music via any Chromecast enabled devices. It does not pertain to controlling Hubitat connected devices with Google Assistant or a Google Home devices. Google Assistant Relay I think you mean, is a node.js application that runs on a separate computer or Raspberry Pi. For TTS, yes it does only support broadcast announcements, and it has a terrible prefix that cannot be removed now. However, its real value is to be able to silently control devices attached to Google Assistant by sending TTS messages to it from Hubitat. You simple prefix them with [CC] and Google Assistant will control many devices they support as if you had spoken to your phone or Google Home out loud. If you prefix the TTS message with [CCC], it will do the command, but will also give you feedback.