Recover deleted messages

go to Settings > [your name] > iCloud and check the switch position for Messages

If the switch is ON, then you cannot recover your deleted messages. (no need to read any further)

If the switch is OFF, then you might be able to recover your messages IF you have an iPhone backup that contains the messages you are trying to recover. In which case you'd need to restore your iPhone to that backup. In doing so, you'd likely lose some data between now and whenever your backup occurred.

If you have the switch on your phone set to save forever.. then yes they will save forever.. until you delete them.

iCloud is not a back up for your messages. It's for syncing them with your other devices.

The important thing to note with the switch, is that the position of it dictates whether your Messages are included in an iPhone backup. if the switch is on, then iPhone backup does not bother saving the messages because they are stored in iCloud. (same deal with iCloud photos)

About backups for iPhone, iPad, and iPod touch - Apple Support

Even if you had that switch turned off so that your iPhone backups contained your Messages, every time the phone backs up it replaces the prior backup. so you would have to specifically set aside an iPhone backup that contained your messages in order to recover them. (called 'Archiving' a backup)

They are saved until you delete them. If you delete them, it is reasonable to assume you don't want them any more. If you want to protect yourself from your own deletions, you need to separately backup your phone.