Heat 1 cup plain water to steaming in a medium saucepan. Remove from heat; stir in agave syrup and 1/3 cup each small thyme, rosemary, and sage sprigs. Let stand about 1 hour, stirring often to release flavors. Strain syrup into a large pitcher, pressing out liquid. Stir in lemon juice.
Arrange large thyme, rosemary, sage, and basil sprigs in a pitcher (at least 2-qt. size), crushing them lightly with your hands. Pour in syrup, sparkling water, and 2 cups ice.
Tie 6 small bouquets of remaining herbs with kitchen twine and set one in each glass along with a lemon wedge. Pour in spritzer.
Make ahead: Through step 1, up to 1 day, chilled airtight.