This is all dependant on you having "Save history when conversations are closed" checked in Messages prefs - otherwise you can find the conversation, but not rejoin it to your main chat window.
The procedure is different if "Messages in Cloud" is enabled, which unchecks & disables the "Save History…" pref.
Both versions below [edited heavily over time].
I have retested this Jun 2022, with "Messages in Cloud" enabled…
Switch your phone off.
Log out of Messages on the Mac then quit the app
Navigate to ~/Library/Messages/
Enter Time Machine & navigate back in time until before your error.
Select the chat.db file & restore
[alternatively grab this file from any other backup, Backblaze etc.]
Reboot, open Messages & check messages are restored.
Boot the phone
If you're lucky, you should be back to sanity.
Without "Messages in Cloud enabled…
You cannot directly re-open the last conversation you had from the app itself, if you already closed it by hitting the x.
You need to dig in history, it's located at
Conversations are stored by date. You only need to find any one instance of the conversation you are looking for.
Double-clicking that file will reopen it in a separate window in Messages.
Keep that window open, or the next step fails.
To persuade it to reattach to the main window…
Scroll down your conversations list - it will have reappeared in last place.
Select it, it will appear to be empty, but will fill as soon as you click it.
You can now close the extra window.