Does PURE have a long U vowel sound?

No, "PURE" has a long U sound, which is represented by the symbol /juː/.

This sound is different from the long U sound in words like "flute" or "rule", which is represented by the symbol /uː/.

The /juː/ sound is a combination of the /j/ sound (as in "yes") and the /uː/ sound. This is why the "U" in "PURE" is sometimes referred to as a diphthong.