Let’s assume that we’re just replacing our sun with a pair of stars which are in a stable orbit around each other, each of which is half the size of the sun, because if our replacement stars are in unstable orbits, this will get super complicated really fast. Even with this simplifying assumption, our solar system would be a very different place.
A star’s energy output is strongly related to how much mass it has, but it’s not a one to one relation. If you cut the sun’s mass in half, you reduce its brightness by 90%. Gravity doesn’t have as much mass to work with, so the force of gravity can’t crush the star down as much, and the star can’t reach the same pressures and temperatures in its center as a more massive star can. These half-stars are at the upper edge of what’s considered a red dwarf star; they can still burn hydrogen in their cores, but at a much slower rate than our sun. Slower energy production gives you a dimmer star, and a dimmer star means a cooler, redder star.
This means, therefore, that if you cut the sun’s mass in half, you go from a star that looks yellow-white, and has a surface temperature of 5800 Kelvin (9980 F, or 5527 C) to something that will look distinctly orange, tipping towards the red end of orange. Each of these half-suns would have a surface temperature of only 3700K (6200 F or 3426 C), a drop in surface temperature of 40%.
Our replacement set of stars has a combined energy output of 20% what our sun’s brightness is. As a result of this drop, the other thing that will definitely change about our solar system is the distance from the stars where liquid water can pool on the surface of the planet. With 20% the output of our current sun, Earth would be way too far away from these stars - all the water on our planet would freeze. In fact, the habitable zone would be almost exactly where Mercury’s orbit is now. Mercury’s orbit goes between 0.3 and 0.46 AU (AU being the distance between the earth and the sun). The habitable zone would range between almost these same numbers: 0.32 AU, if the planet was getting light from only one star, up to 0.44 AU, if it was getting sunlight from both of them.
Mercury is really close to the sun. So if we put our habitable planet in the right spot to have life, it will also have to be really close to the two half-suns. But then you start getting into really hairy territory, because any time you have three objects interacting with each other, as you would with a close pair of stars and a nearby, light planet, the orbits can get pretty funky - this is called the 3 body problem. It’s not nearly as nice as having one massive object in the centre for things to calmly orbit around. There are windows of stability, where the stars and the planet can orbit relatively calmly for a long enough time to develop life. The positions of these windows depends entirely on the exact configurations of the orbit of the two stars in question. If the planet is not in a window of stability, one of your three objects can wind up getting tossed out of the solar system, which would be particularly bad for the planet you’re trying to grow things on.
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