TypeScript 4.4.3 extended mapped types in generic functions

example.ts

// Approaches 1-3 do not work, yielding errors in each of the functions.
// Approach 4 seems to work.

type MappedWithExtra1<T extends Record<string, unknown>> = {
	[K in keyof T]?: string;
} & { extra?: string };

type MappedWithExtra2<T extends Record<string, unknown>> = {
	[K in keyof T as K | 'extra']?: string;
};

type MappedWithExtra3<T extends Record<string, unknown>> = {
	[K in keyof T | 'extra']?: string;
};

type MappedWithExtra4<T extends Record<string, unknown>> = {
	[K in keyof (T & { extra: string })]?: string;
};

const x = { a: 1 };
type X = typeof x; // { a: number }
type XK = keyof X; // 'a'

const f1 = <T extends Record<string, unknown>>() => {
	const v = {} as MappedWithExtra1<T>;
	v.extra = '';
	const k: keyof T = 'k';
	v[k] = ''; // Type 'string' is not assignable to type 'MappedWithExtra1<T>[keyof T]'. ts(2322)
	let s: MappedWithExtra1<T>[keyof T];
	s = ''; // Type 'string' is not assignable to type 'MappedWithExtra1<T>[keyof T]'. ts(2322)
};

let s: MappedWithExtra1<X>[keyof X]; // string
s = '';

const f2 = <T extends Record<string, unknown>>() => {
	const v = {} as MappedWithExtra2<T>;
	v.extra = ''; // Property 'extra' does not exist on type 'MappedWithExtra2<T>'. ts(2339)
	const k: keyof T = 'k';
	v[k] = '';
};

const f3 = <T extends Record<string, unknown>>() => {
	const v = {} as MappedWithExtra3<T>;
	v.extra = ''; // Property 'extra' does not exist on type 'MappedWithExtra3<T>'. ts(2339)
	const k: keyof T = 'k';
	v[k] = '';
};

const f4 = <T extends Record<string, unknown>>() => {
	const v = {} as MappedWithExtra4<T>;
	v.extra = '';
	const k: keyof T = 'k';
	v[k] = '';
};