After Qin Shi Huang unified China, the character 玺 was reserved exclusively for the emperor's seal. All other seals were called 印 (yìn). The legendary 传国玉玺 (Imperial Seal of China) was carved from the He Shi Bi jade.
Jade at the base is literal - imperial seals were carved from precious nephrite, most famously the legendary 传国玉玺 said to have been cut from the Heshi jade. The radical thus does both etymological and material work, anchoring the character in royalty.
Sits on top and supplies the sound. The traditional form 璽 had a fuller phonetic 爾 above; simplification reduced it to 尔 in 1956, and the reading drifted further from ěr to xǐ. Pure sound clue, no semantic role here.
