No, tofu should not be layered with herbs during storage. Store tofu submerged in fresh water in an airtight container in the refrigerator.
Tofu is best stored in water to maintain its moisture and prevent it from drying out. The water should be changed daily or every other day to keep the tofu fresh. Storing tofu with herbs can introduce bacteria and affect the tofu's flavor and texture negatively. The goal is to keep the tofu as clean and neutral as possible until you're ready to use it. Proper storage ensures the tofu remains firm and doesn't develop an off-putting taste.
If you're not planning to use the tofu within a few days, consider freezing it. Freezing changes the texture, making it chewier and better at absorbing marinades, but it also extends its shelf life significantly. Thaw it in the refrigerator before using.