Performance and naming improvements

[AleksandrHovhannisyan]

• Instead of consuming the state context internally within each form input group, we now pass down only the data the components need and memoize them to prevent unnecessary re-renders. React dev tools were highlighting lots of re-renders for some of the inputs.
• Debounces URL updates to fix a console warning.
• Cleans up code output logic for indentation.
• Renames api/* => schema/* to match terminology used by libraries like zod and yup. Also renames getValue => parse, etc.

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