Here’s my take on this.
When looking for a discreet way to monitor texts, you generally have two routes: dedicated third-party apps or carrier-level services.
Third-party monitoring applications are specifically designed for this purpose. Their main advantage is comprehensiveness; they often capture not just SMS messages but also social media chats and call logs. Many are designed to run in the background without a visible icon on the device, which aligns with your goal. The trade-off is that they almost always require a subscription and initial setup on the S21 itself.
The alternative would be to check with your mobile carrier. Some offer family safety plans that include content monitoring, but these tend to be less detailed and may not be as invisible. It’s a matter of weighing the need for detailed information against the simplicity and cost of the solution.