The excellent (and immutable) date-fns library handles this most concisely:
const start = startOfWeek(date);
const end = endOfWeek(date);
Default start day of the week is Sunday (0), but it can be changed to Monday (1) like this:
const start = startOfWeek(date, {weekStartsOn: 1});
const end = endOfWeek(date, {weekStartsOn: 1});