Panna Cotta with Balsamic Strawberries

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1/2 packet (1 teaspoon) unflavored gelatin powder

1 1/2 tablespoons cold water

1 1/2 cups heavy cream, divided

1 cup plain whole-milk yogurt

1 teaspoon pure vanilla extract

1/2 vanilla bean, split and seeds scraped

1/3 cup sugar, plus 1 tablespoon

2 pints (4 cups) sliced fresh strawberries

2 1/2 tablespoons balsamic vinegar

1 tablespoon sugar

1/4 teaspoon freshly ground black pepper

Freshly grated lemon zest, for serving