How to find the Orbital Period of two Binary Planets around a Single Star?
I think that at the moment, all you have available for the pair's orbit around their star is a snapshot of their two distances; 964 and 989 seconds, or about 289 and 297 million kilometers. Your snapshot doesn't have any velocity information, so I think that there's no way to calculate the mass of the star from that data. Since the first planet is 2000 times heavier than the second, lets say that the pair's center of mass is 289 million km from the star.
However your second link states explicitly that the star is 1.0195 solar masses. That means that the standard gravitational parameter or $GM$ is about 1.352E+20 m^3/s^2, so using

$$T= 2\pi\sqrt{\frac{a^3}{GM}}$$

I get a year of about 972 days for the center of mass of the pair. Since the lighter planet oscillates by +/- 10 million km (its semi-major axis) every 80 days, that's a 7% amplitude change in distance to the star or roughly a 14% amplitude modulation of the brightness of the sunlight every 80 days, so that may have some impact on the weather for the smaller planet.

Interestingly, the smaller planet goes "around the world in 80 days" if we name the larger planet "world".