How is this function (server, options) used?
I suppose there is some call to Hapi that registers the plugin?
I think that registration call should be the ServerDefinition.

I agree it can be made more precise by using the registration as definition...

The docs say:

At their core plugins are an object with a register property, that is a function with the signature async function (server, options). Additionally the plugin object has a required name property and several optional properties including version.

For example:

function after(server, options) {
  server. Route([
    {
      "method": "GET",
      "path": "/authenticate/{id}",
      handler(request) {
        ...
      }
}

function register(server, options) {
  server.dependency(options.dependencies || [], server_ => after(server_, options));
}

exports.plugin = { register, pkg };

and

const myPlugin = {
    name: 'myPlugin',
    version: '1.0.0',
    register: async function (server, options) {
        ...
    }
};