In a medium bowl, whisk together the flour, baking powder, and salt.
In a separate, large bowl, beat together the oil and sugar until combined.
Add the eggs, lime juice, lime zest, vanilla extract, tequila, and yogurt, and beat until smooth.
Add in the flour mixture and beat until just combined.
Divide the batter evenly into the cupcake liners, filling each about ⅔ full.
Bake in the preheated oven for 20–23 minutes, until a toothpick inserted in the center comes out clean. Let them cool in the pan for 5 minutes, then transfer to a wire rack and cool to room temperature.
While the cupcakes are baking, place the water and sugar for the syrup in a small saucepan. Heat over medium heat, stirring occasionally, until the mixture begins to boil.
Remove from heat and stir in the tequila and lime juice. Let cool completely.
Use a pastry brush to brush the tops of the baked cupcakes with the syrup.
Add the softened butter and cream cheese to a large bowl and use a hand mixer or stand mixer to beat until completely smooth.
Add the powdered sugar to the bowl and beat until combined.
Add in the tequila and lime juice, and beat until the frosting is light and fluffy.
Frost the cooled cupcakes.
Garnish with lime slices, lime zest, and flaky sea salt, as desired, to serve.