Our sun's rotation period is 24.47 days at the equator and almost 38 days at the poles, our planet's rotational period is 23h 56m 4.098,903,691s. Use of Schwarzschild equations for either case isn't exact.
If you used the equation for non-rotating objects to calculate the time at the altitude of GPS satellites (~ 20,200 km or 12,550 miles) then you would be off by 38,636 nanoseconds per day. A Julian year is defined as 365.25 days of exactly 86,400 seconds (SI base unit), totalling exactly 31,557,600 seconds in the Julian astronomical year. The Gregorian calendar year (400 year average) is 365.2425 days.
Multiplying 365.2425 x 38,636 = 14,111,509.23 nanoseconds, that's 0.0141 seconds per year. If being off by that amount isn't of any concern to you then you can use the easier equation, such as for calculations involving the star HR 1362 which has a rotational period that is 306.9 ± 0.4 days.