In Chinese culture, a 手稿 (shǒugǎo) holds a significance that often transcends its functional purpose as a mere draft. Due to the artistic and philosophical importance of calligraphy (书法, shūfǎ), the handwritten manuscript of a respected writer, scholar, or historical figure is considered a valuable piece of art in itself. A good Western comparison is the value placed on an original painting by a master versus a print. However, for a 手稿, the appreciation is twofold: it's valued for the intellectual content and for the aesthetic quality of the handwriting, which is believed to be a direct expression of the author's character and spirit. For example, the manuscripts of the famous 20th-century writer Lu Xun (鲁迅) are treated as national treasures. Scholars and enthusiasts study not only the changes he made to the text but also the energy and style of his brushstrokes. This contrasts with a more typical Western view where a manuscript is primarily a utilitarian object—an important step in the publishing process, but ultimately superseded and made obsolete by the final printed book. In China, the 手稿 can sometimes be considered even more precious than the published work because it contains the “raw energy” (气, qì) of the creator.
手稿 (shǒugǎo) is a specific and somewhat formal term. You wouldn't use it to describe your rough notes for a school presentation. It's reserved for works of literary, artistic, or academic importance.
The connotation is almost always neutral-to-positive, implying value, authenticity, and importance.
The most common mistake for learners is confusing 手稿 (shǒugǎo) with similar-sounding words for “draft.”