Initially you could only log in from one device, as it created a new private key every time you switched device. Then they implemented Whatsapp Web, which essentially required the primary device to be connected to the internet, the chats would then be transferred from the primary device to the secondary devices (I assume through an encrypted tunnel of some sorts). Then as of late they have implemented a new technology that allows you to share your private key among multiple devices, making them all the “primary device”. The chat history and all the messages can be shared from one device to another while encrypted. The weak spot at one point was the chat backup, which was unencrypted and stored in your Google Drive, so technically Google could have had access to all your chats. Today though, you can encrypt the backup through a password.
In theory Whatsapp has never needed to read your chats to have the functionality it has. That’s in theory because it’s closed source and we cannot know anything for certain. All this is just what Meta/Whatsapp said or pure speculation.