Sealed into the very first block of the chain — forever, unchangeable.
This page doesn't store the message — it asks the live ETH II blockchain for its
first block (block #0) the moment you load it, and decodes the message
right in your browser. You can do the exact same thing yourself:
Send this request to https://www.ethii.net/rpc:
{"jsonrpc":"2.0","method":"eth_getBlockByNumber","params":["0x0",false],"id":1}
Take the extraData value it returns, drop the 0x, and paste it
into any free “hex to text” converter. You'll get the same message you see above.
The message can never be edited: the genesis fingerprint (hash) is calculated from every field in the block, including this message. Change one letter and the fingerprint changes — and that node is no longer on the ETH II chain at all.