Refrigerate or not refrigerate?
If your tomatoes are not fully ripe, leaving them at room temperature will enable them to ripen naturally, which helps maintain their flavor and texture.
Once the tomatoes are fully ripe, you can refrigerate them to extend their shelf life. However, refrigeration can sometimes alter their texture and dull their flavor, so it's best to bring them back to room temperature before using them.
To avoid this, only refrigerate fully ripe tomatoes if you don't plan to use them within a couple of days. If you have a surplus of tomatoes and want to preserve their taste, consider canning, freezing, or drying them, which allows you to enjoy their flavor for much longer.
This detailed article provides in-depth information on washing and storing fresh tomatoes (and store bought too).