What is a 'star rose'?

Solution 1:

As JavaScript’s star rose

This means "as Javascript became more popular."

Rose is the past tense of rise, and not the flower. Javascript is becoming a rising star, i.e. more popular.

Solution 2:

This shouldn't be seen as a single phrase "star rose", which seems to imply the rose of a star, but rather, "rose" as the verb, and "star" as the noun.

"Star" here refers to the popularity and fame of Javascript. "Rose" refers to the fact that the popularity and fame of Javascript is increasing ("Rose" as in "rise" past tense). Thus, read:

As Javascript's fame increased (star rose)

I hope that helps.