This is disabled by default in iOS 13, to keep your messages secure (and because often times it doesn't work properly). You have to go into iCloud settings to turn it on. And then if you aren't using iCloud Backup, the key to your Messages backup is not stored by Apple, so they can't read it anyway (see https://support.apple.com/en-us/HT202303).

For some reason, I doubt Google would do that.