Combine the water, honey, and sliced ginger in a small saucepan and bring to a gentle simmer over medium heat, cooking for 8–10 minutes until the ginger is clearly aromatic and spicy but not harsh, then remove from heat, add the lemon zest, cover, and let steep for 10 minutes more before straining and cooling completely.
Add the lemon pulp to a large pitcher and gently muddle just until juice is released and light structure forms, keeping the mixture loose and avoiding a purée.
Add the fresh lemon juice, about 120 ml of the cooled ginger–honey syrup, and the pinch of fine sea salt to the pitcher, then stir until fully combined and taste, adjusting with more syrup for heat or sweetness if needed.
Just before serving, gently pour in the ice-cold club soda and stir lightly once or twice to integrate while preserving carbonation, adding a small splash more soda if the flavor feels too intense.
If needed, refrigerate briefly, but always add the club soda at the very end to keep the drink lively.
Fill glasses with ice, pour over the sparkling ginger lemonade, and garnish with lemon slices and optional thin ginger slivers.
