The "browser" is a blank execution sandbox with a rendering context. The remote server sends programs (using something like WASM) with a standardized ABI. The program can use the rendering context to put stuff on the screen or receive user input.

Indexing and page interoperability is done by exposing standard functions which yield the necessary metadata. For example, if you want your site to be indexable by a search engine, you expose a function "contentText()" which crawlers will call (and which the client browser might also call and display using the user's own reader app). In the simplest case, the function simply returns a literal.

Core resources like libraries would be uniquely identified, cryptographically signed, versioned, and shared.

If someone wanted to make use of a browser pipeline like the standard one we have today, they might send code which does something like "DOMLibrary.renderHTML(generateDocument())". But someone else could write a competing library for rendering and laying out content, and it might take hold if it's better, and it wouldn't have to be built on top of the first one.

Also, the browser wouldn't necessarily be a separate app (though someone could make one); it would be a standard built-in feature of operating systems, i.e. the sandboxing would be done at the kernel level. With security properly handled, there'd be no difference between a native app and a web app, except whether you load it from your own filesystem or a remote one.