In my world, I have a binary S-type Solar System of Star-A and Star-B with these properties:
Star-A: Luminosity: 0.86822 Sol / Mass: 0.98097 Sol / Radius: 0.91958 Sol / Radius of Hill Sphere: ~37.218 AU
Star-B: Luminosity: 0.108 Sol / Mass: 0.61342 Sol / Radius: 0.70387 Sol / Radius of Hill Sphere: ~27.216 AU
The Semi-Major Axis between them is 77.8 AU (I know about the barycenter, it exists but the details aren't important about it), with an eccentricity of 0.41, so the closest distance between them is around ~45.9 AU and the farthest is ~109.7 AU.
That will cause an interaction between the Hill Spheres of both stars when they are close, so It will shrink the hill sphere of Star-A to ~18.7 AU (After that the interaction will begin) and for Star-B to ~8.68 AU.
Star-B will have Planet-X with Mass: 1.15 Earth / Radius: 6689.55 km / Eccentricity: 0.012 / SemiMajorAxis: 0.33 AU/ Earth-Like temperature
and it has a big Moon (Let's call it Moon-X) to break the tidal-looking with Mass: 0.328 Earth (Yea Earth) / Radius: 4469.2 km / SemiMajorAxis between Planet-X and Moon-X: 70157 km (Another barycenter that I won't write about...) and since both Planet-X and Moon-X are tidally-looked they have the same day period of ~42.25 hours.
Moon-X got there like Our Earth-Theia(Moon) scenario.
Moon-X is big enough to have an atmosphere but doesn't have tectonic plates, so it's similar to Venus's atmosphere (Because of the Carbon Cycle) and will have a dense atmosphere of CO2 with a bit of N2 and a pressure of 32 atm at its surface level? (like Sea level on Earth)
So how plausible is this? and if the binary star isn't plausible u can ignore it and use Star-B alone with its double-planet.
And in case if u wonder why I need an S-type system to be this close, it's because when Star-A and B are close, Star A will be to Planet-X like our Sun to Pluto, which "At noon, the sunlight would be strong enough for you to read a book."