If you login to your account on your Snikket server on all the devices you have at home, and you remain logged in for all the time you use your Snikket server, everything will be synced over all these devices.

Let me explain it further. You login to your Snikket server on 3 devices (desktop, laptop, and smartphone) and you use only these 3 with no re-installing the operating system and not factory resetting the smartphone, you will keep getting the history on these 3 devices - synced.

But you decide to try out a new XMPP client, let say monocles chat. Since that client is new for your account, that client will get its own encryption key. Because of this, monocles chat can not read anything you and the contacts you have communicated with. This also applies when you re-installing the OS or do a factory reset.

End-to-end encryption 101.

Let say this would not be the case and monocles chat do see the history of all of your chats, that data must remain on the server and can be decrypted by the new client with maybe a master encryption key of some sort. This is not end-to-end encryption 101. That would be a security breach.

However, letting you export the chat history from the other clients and importing the chat history to monocles chat, that would be much better. Because then it is you who decides if you want to keep the chat history or not. You will be in control over your own data. This is a feature I miss in XMPP clients.