when the component is in prerender mode, there is no connection to the browser, so no javascript interop is allowed. prerender will only have access to site cookies, which you could use instead of local storage for prerender.
to implement pre-render, on the host page request, the server creates an instance of the BlazorApp, and builds and renders the tree. the tree is converted to html, and the app is shut down. the html is rendered into the app div (along with persistent state json). The browser loads the page, renders the html, and loads the blazor bootstrap js. this js loads the wasm, or opens the signal/r connection and starts a new blazer server instance.
to access local storage (or any jsinterop) you use the OnAfterRender{Async} override. this will only fire with blazer app instances tried to a browser.
note: you can use the cascading parameter HttpContext to detect prerender:
[CascadingParameter] HttpContext HttpContext {get; set; }
bool IsPreRender => HttpContext != null;