Why am I being charged for a stopped Amazon Lightsail instance?

You're still being charged for your stopped Lightsail instance because stopping an instance doesn't stop the billing. Unlike some other AWS services, Lightsail instances continue to incur charges even when they're in a stopped state.

This happens because even though the instance isn't running, AWS is still reserving the compute resources, maintaining your data on the attached storage, and keeping your configuration intact so you can easily restart it when needed.

To completely stop charges for a Lightsail instance, you need to delete it entirely. If you want to preserve your work, you can create a snapshot of your instance before deleting it (though snapshots do have a small storage cost of $0.05 USD/GB-month). This way, you can recreate the instance from the snapshot when you need it again.

Also, check if you have any other Lightsail resources that might be generating charges, such as static IP addresses, which continue to incur costs even when not attached to a running instance. In fact, there was a case where a user continued to be charged for Lightsail after deleting their instance because they still had a static IP resource in their account.
Sources
Billing and account management - Amazon Lightsail
Why am I still being charged for Lightsail? | AWS re:Post
Need Layman's terms clarification on free tier | AWS re:Post