Update : After looking more at the code, I found that this feature may be a tablet specific thing because Android tablets currently use the Web version of messages (Inside Google Message app) to sync messages. While there is nothing stopping Google from bringing to phones as well but we will see more about it in future updates of Google Message. 

Google will make it easier for you to send and recieve your RCS chats/messages from Google Messages on your other phones/devices. With the latest beta version of Google Messages, Google is working on adding this functionality.

Currently there is no way to read/send your RCS chats/messages on your other phone. But there is a workaround which involves using Google Messages in your phone browser and turn on desktop website option to pair using QR code. With the latest update of message you don't have to do that anymore.

An newly added illustration related to the new feature.

Google will use your phone number for this functionality which is expected because all your RCS chats are linked to a phone number which Google automatically verifies when you opt into using RCS chats. In Google message I found some strings such as -
Use your phone number to send and receive messages on devices signed into your Google account.
Message from your phone number on your other devices
There are two things needed here for it to work - your phone number and other devices with the same Google account. Google previously didn't allow using the same phone number on two devices with Google messages and it is great to see them bringing this functionality and bring a true multi device experience. This may be useful on the Pixel Tablet which have Google message app but relies on Google Web version for checking your messages (The usual QR code pairing process).

Currently the feature may be in work because I don't have other device to test and there is no flag for this thing which I can turn on. So people can try the message version messages.android_20230907_01_RC00.phone.openbeta_dynamic and check if it works. (update: I tried to see if it works using my account on my friend's phone with the same beta version, but looks like some pieces of the puzzle are missing and I can not get it to work. ) 

In addition to the above feature, Google Messages will show you a warning screen when a screen reader is active.
Screen reader active
"We suspect that there's a screen reader active on your device. Your content will be accessible once it is turned off."

I am looking more into this and will update if I find anything new. For more feature leaks and feature flag updates join Gapps Flags and Leaks on telegram.