How to infer value type iusing using "dotted path" inside interface

I want to create generic interface for table column

And I want typescript infer type of 'value' inside 'render' by using 'field' (that uses "dotted path")

But it inferred that 'value' has type of all values of RowData What I do wrong ?

type Paths<T, K extends keyof T = keyof T> = K extends string
    ? T[K] extends Record<string, any>
        ? T[K] extends ArrayLike<any>
            ? `${K}.${Paths<T[K], Exclude<keyof T[K], keyof any[]>>}`
            : `${K}.${Paths<T[K], keyof T[K]>}`
        : K
    : never;

type FieldValue<T, Path extends string> = string extends Path
    ? unknown
    : Path extends keyof T
    ? T[Path]
    : Path extends `${infer K}.${infer R}`
    ? K extends keyof T
        ? FieldValue<T[K], R>
        : unknown
    : unknown;

type Flat<T> = { [k in Paths<T>]: FieldValue<T, k> };

export interface TableColumn<D, K extends keyof Flat<D> = keyof Flat<D>> {
    title: string;
    readonly field?: K;
    render?: (options: { row: D; value: Flat<D>[K] }) => string;
}

interface RowData {
  a: number;
  b: {
    c: string
  }
}

const d: TableColumn<RowData> = {
    title: 'Title',
    field: 'b.c',
    render: ({ value }) => value // value type is string | number but expected string because  RowData['b.c'] is string
};

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