After clicking it a notification should pop up to let the player check how much to recharge.

Asking in this comment: How do you check what's sold and sold to whom in the shop you setup?

To answer your question about shops, you just close the shop then speak to Fredrick.

Added, and live now! NPC shops have a new Recharge All button under SELL ITEM. It shows whenever any of your stars or bullets aren't full. Clicking it asks you to confirm the total cost first, like you suggested (for example 'Recharge all 40 stacks for 12,345 vesos?'). If you can't afford all of them, it tells you how many you can afford and asks if you want those. Every stack refills in one go. Refresh the game to get the update.