AsyncIOIntegration cause misbehavior in transactions created from auto-integrations

### How do you use Sentry?

Self-hosted

### Version

2.38.0

### Steps to Reproduce

When using AsyncIO Integrations with auto-integrations found in dependency file, such as FastAPI dependency, tags explicitly set on automatically created traces from the auto-integrations, (eg: API transactions) do not show up. However, tags do show up on manually created transactions.

For reference, the Sentry SDK is initialized asynchronously alongside the FastAPI app using asyncio

### Expected Result

Tags should show up on all transactions whether they are automatically created from auto-integrations or manually created using the Sentry SDK.

### Actual Result

Transactions created from auto-integrations do not have the created tags on them