Object.keys returns string[] not Array<keyof T> (where T is the type of the value passed in). The reasons for this are outlined here.
Since your object is probably not going to have unknown keys, you can use a type assertion:
export type Period = 'dy' | 'wk' | 'mn' | 'qt' | 'yr';
const periods: Record<Period, string> = {
dy: 'Day',
wk: 'Week',
mn: 'Month',
qt: 'Quarter',
yr: 'Year'
};
const key = (Object.keys(periods) as Array<Period>).find(key => periods[key] === 'Day');
Playground Link