All my Chrome extensions do not collect data and as such do send it to any server.
Some of my extensions use Chrome’s shared storage so that your settings are shared between chrome instances on different machines. This is a priavte data store privided by Chrome and completely out of my control. I do not have access to this data other than from within each Chrome extension.
If you need any points clarifying, please contact me. There’s an Email ark link on the left there.