in addition to the addon, NVDA+tab might help in some cases.

Couldn’t you just arrow or go back to it and read it again. Super easy to achieve.

It is very much possible.

Depending upon the app you are using, you might be able to simply do up and down arrow on the messages to read the current message again. Text review with numpad keys or nvda+shift left/right arrow keys might also help if you are using laptop layout keyboard.

If none of the previously mentioned options work, then I suggest you to install Speach history addon. In fact, below, I am pasting the text giving info about the addon, which I copied using that addon itself.

Add-on Information dialog Speech history review and copying (speechHistory)Version: 2022.1Author: Tyler Spivey, James ScholesDescription: This add-on allows you to review the most recent strings spoken by NVDA, by default using Shift+F11 and Shift+F12. Additionally, you can copy any spoken item to the clipboard by pressing F12. Use the settings panel for the add-on to increase or decrease the maximum number of stored history entries, and decide whether whitespace should be trimmed from the start or end of text. Use NVDA's Input Gestures dialog to change the supplied keystrokes.URL: $1Minimum required NVDA version: 2019.3Last NVDA version tested: 2022.1

Edit: direct download link for this addon is: https://github.com/jscholes/nvda-speech-history/releases/download/v2022.1/speechHistory-2022.1.nvda-addon

NVDA doesn't have anything like that as far as I know. Specify where you want it to happen so I can help better.

Press nvda+n and go to Tools >Speech Viewer. After you open it, it'll log everything the screen reader reads so you can re-read it or copy it.
You can also set a shortcut to quickly open Speech Viewer by adding it in Preferences >Input Gestures, under the Tools section.

Which program do you want to re-read messages in? Perhaps there is an easier way to do that, by just scrolling back to the message.