Messages app on iMac would not open because "it was downloaded on an unknown date." I deleted it, but now I need to reinstall the app.

What year model iMac and what macOS is it running?

see > Identify your iMac model - Apple Support

Messages is part of macOS and virtually impossible to delete.

Try this, navigate to your Applications Folder and open that version of Messages to see if it works.

You should not have been able to delete the Messages application in Ventura that is part of the macOS installation. Now, you will have to reinstall macOS Ventura to get that Messages application back. There is no separate download for it.

You’re welcome.

To keep the newly opened Messages icon on your Dock > Control (right) click on the icon > select Option > Keep in Dock.