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星 contains the radical 日 meaning sun/day. This makes sense from a modern understanding, as it is well known that the sun was a star. However, it appears this has only been known since the 19th century, suggesting that the connection is not so intuitive.
How did the 日 radical come to be used here? Was there an understanding that the sun was the same/similar to a star, or was there another reason for this?
No, because「星」was not the original character for the word meaning star.
「星」was originally written「晶」:
These are oracle bone script samples, and by that stage stars were already characterised as being more numerous and smaller than the sun and moon, hence the appearance.「晶」now means sparkling/crystal/radiant, and this is a semantic extension from the original meaning twinkling stars.
Later on, a sound hint「生」was added (note, the common On'yomi for both「星」and「生」, which are both しょう and せい, are identical).
The number of stars depicted ranged from 2-5, but eventually settled on to 3:
The right hand side is the modern representation of the form on the left.
A Warring States innovation simplified it to one star,
and this is what we're left with today.
To clarify, there was a clear recognition that「星」and「日」were both celestial bodies shining in the sky, as seen by the structural composition of「晶」, but「星」is also the same term given to planets and comets, and the philosophical/cultural/religious significance of the sun itself, seen in words like「太陽」(literally Grand Yang, by far the more pervasive word for sun in Chinese), is not accorded to「星」.
A comment rather than an answer; the assertion that "the sun was a star [...] has only been known since the 19th century" is not maintainable. Quote Wikipedia on Stars (emphasis mine):
In 1584, Giordano Bruno suggested that the stars were like the Sun, and may have other planets, possibly even Earth-like, in orbit around them, an idea that had been suggested earlier by the ancient Greek philosophers, Democritus and Epicurus, and by medieval Islamic cosmologists such as Fakhr al-Din al-Razi. By the following century, the idea of the stars being the same as the Sun was reaching a consensus among astronomers.
Also note that supernovae were a known phenomenon to the Chinese of 2000 years ago:
In spite of the apparent immutability of the heavens, Chinese astronomers were aware that new stars could appear. In 185 AD, they were the first to observe and write about a supernova, now known as the SN 185. The brightest stellar event in recorded history was the SN 1006 supernova, which was observed in 1006 and written about by the Egyptian astronomer Ali ibn Ridwan and several Chinese astronomers.
This gives a wholenother time horizon to the history of concepts than the notion of '19th century' would suggest.
I otherwise second what @drooze writes, and just want to add that the really interesting question is, why didn't the ancient Chinese develop a simple sign for 'star' when they did so for e.g. 云 cloud, 日 sun, 月 moon, 天 sky?—The Egyptians certainly did have two distinct signs, viz. 𓇳(𓇶) sun (with rays) vs 𓇼 star.—Given the plethora of simple signs for things of importance in the historical record and the demonstrable early Chinese interest in meteorological and celestial phenomena, shouldn't one expect a simple graph for 'star' right next to 日 and 月?
