The two are more independent of each other than that. As you increase the power to the shaft, the generator moves forward relative to the grid, increasing the power angle delta. Power transmitted from the generator to the system is the product of the absolute values of the generator internal voltage and the system voltage divided by the reactive impedance between the two voltages, all multiplied by the sin of delta. So, with constant voltages, more power means a higher delta. All power comes from the shaft, the field can not produce power.
With the shaft supplying a constant power, changing the internal voltage produced by the generator will change the power angle, but will not change the amount of power.
The amount of reactive power is the product of the magnitudes of the two voltages divided by the reactive impedance, multiplied by the cos of delta, all that minus the square of the magnitude of the system voltage divided by the reactive impedance. Increasing the internally generated voltage (increasing the field current) increase the reactive power delivered by increasing the product of the magnitudes of the voltages. In response to that increase the power angle reduces so that the real power output remains constant (controlled by the power in at the shaft). The reduction in power angle increases the cos value, so reactive power output goes up with both the increase in generated voltage magnitude and with the decreased power angel.
If someone else knows how to put the equations in here so they show up well formatted, that would be great.