0.5625-18UNJF is the inch notation of 9/16-18UNJF.
Even with 9/16-18UNF taps, the shape of the internal thread is the same, so if the accuracy is correct, machining is possible.
(The pilot hole diameter of the UNJF must be varied from the size of the UNF.) )
However, you need to pay attention to the thread accuracy.
Screws with a "J" like UNJF are aircraft screws, and the thread accuracy is often 3B class (equivalent to 1st class).
OSG's standard stock products are aimed at the equivalent of 2nd grade. If the drawing instructions are 2B, the taps can be shared.
In order to achieve an accuracy equivalent to the first grade of 3B, it is extremely difficult to produce it with a tap with a precision that is made for the second grade (2B).
It is better to use a tap made with the accuracy of aiming at 3B to avoid defects.