`${number}` template literal type does not allow "NaN" or "Infinity"

Bug Report

🔎 Search Terms

NaN Infinity template literal types

🕗 Version & Regression Information

4.3.0-dev.20210226

⏯ Playground Link

Playground link with relevant code

💻 Code

const a: number = NaN //no error
const b: `${number}` = 'NaN' //Type '"NaN"' is not assignable to type '`${number}`'.

const c: number = Infinity //no error
const d: `${number}` = 'Infinity' //Type '"Infinity"' is not assignable to type '`${number}`'

🙁 Actual behavior

compile errors

🙂 Expected behavior

the strings "NaN" and "Infinity" should be valid `${number}`s because NaN and Infinity are valid numbers

Start with the linked TypeScript Playground and the ${number} examples in the issue to reproduce the errors for NaN and Infinity. Trace the compiler's template literal type handling, then add or update the relevant compiler tests so both strings are accepted while existing ${number} behavior remains correct.