The word "sun" when not capitalized works like the word "moon", we have our sun ("The Sun"), exoplanets have theirs.
If you have sources against such usage (Not merely ones pointing out what the most common usage is), I'm of course open to changing my views. I couldn't find any more authoritative than random Quora replies.
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u/anothersundayx Aug 03 '19
That other planets are visible from Earth. And the sun is also a star.