Re binary with Sol, the one planet that is a ‘gas giant’, and has been noted from early in the 20th century, as a ‘failed star’, is Jupiter. Even Sagan posited on that term. So, we may have our binaral twin.
Now, for a ponderance for you:
There was, and still is, the idea of ‘another Earth, 180° opposite this one, with the exact ecliptic orbit, to not be seen from here.
Can you recall what name was given that planet? Hint: it is not this “Nibiru”.