Arabic sharba(t) passed through Persian sharbat and Turkish şerbet before reaching English. The earliest English sense was a cooling sweet drink. Different regional uses later developed into frozen desserts or fizzy powder.
Merriam-Webster records Turkish and Persian as donors. This puzzle follows the route through Turkish; it does not exclude a direct Persian borrowing.
Sources
- Merriam-Webster · sherbet
Dictionary word history; the component and historical references below supply additional detail.
- Online Etymology Dictionary · sherbet
Historical forms, meanings, and context for the route described here.