docs: rewrite README with accurate architecture, portals, and code examples

[FolatheDuckofDuckingburg]

Improves the project README.md by providing precise user portal route documentation (/dashboard, /parent, /educator), accurate localStorage persistence keys, updated TypeScript code snippets, clean Next.js App Router directory structure visualization, and clear setup/build commands.

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PR created automatically by Jules for task 10667949948833352089 started by @FolatheDuckofDuckingburg

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