If you have multiple messages coming in on a consistent basis and ask Google to read them all, you'll notice that those messages which pop up will have the icon for the app which they came from, so you have a visual way of discerning who is messaging you from where. Following this, it will give you a disclaimer that once you enable this, "Google will be able to read all notifications including personal information such as contact names and the text of messages you receive".
To determine whether Google Assistant works on the messaging app you most use, one must wait for a new message from that app and then open Google Assistant by saying "Hey Google".
Google Assistant has always had some measure of integration with various messaging apps; for example, it's long been able to read and reply to Telegram messages (which we use at Ausdroid) but that integration hasn't been complete. Google will tell you however that the message contains audio or an image so you'll know to go look at or listen to whatever it is.
Google Assistant is at the center of the Google ecosystem, which is why Google keeps giving it more and more things to do. Also, once it reads the message, it will ask you if you want to reply to it - which you can both type or dictate. But it wouldn't read messages that you received from third-party apps like WhatsApp and Telegram. WhatsApp, Telegram, Slack, GroupMe, Discord, and Facebook Messenger are among the list of apps that are working.
To make this feature work, you will first need to grant "notification access" to the Google app. Currently, many of us here at Android Police are able to replicate this behavior, so it doesn't appear to be a server-side switch. The Assistant will respond with "this message just contains an audio attachment" when attempting to read a message containing a voice note.
For security and privacy reasons, users are unable to send text messages while their phone lockscreen is on. Notably, Google Assistant rival Siri already has the ability to read out and reply third party apps including WhatsApp since 2016 for individual chats later got the same for WhatsApp Groups in 2018. The Assistant will display the reply in a new card and confirm it's sent the message as well.