docs: update prefect-sqlalchemy async examples to use AsyncSqlAlchemyConnector (#20654)

Author: rcash

docs/integrations/prefect-sqlalchemy/index.mdx

@@ -91,21 +91,8 @@ Use the `SqlAlchemyConnector` as a context manager, to ensure that the SQLAlchem
 
 **Async support**
 
-`SqlAlchemyConnector`  supports async workflows. Just be sure to save, load, and use an async driver, as in the example below.
+For async workflows with async database drivers (like `AsyncDriver.SQLITE_AIOSQLITE` or `AsyncDriver.POSTGRESQL_ASYNCPG`), use `AsyncSqlAlchemyConnector` instead of `SqlAlchemyConnector`. See the **Async** tab below for a complete example.
 
-```python
-from prefect_sqlalchemy import SqlAlchemyConnector, ConnectionComponents, AsyncDriver
-
-connector = SqlAlchemyConnector(
-    connection_info=ConnectionComponents(
-        driver=AsyncDriver.SQLITE_AIOSQLITE,
-        database="DATABASE-PLACEHOLDER.db"
-    )
-)
-
-if __name__ == "__main__":
-    connector.save("BLOCK_NAME-PLACEHOLDER")
-```
 </Note>
 
 <Tabs>
@@ -164,13 +151,13 @@ if __name__ == "__main__":
 
 ```python
 from prefect import flow, task
-from prefect_sqlalchemy import SqlAlchemyConnector
+from prefect_sqlalchemy import AsyncSqlAlchemyConnector
 import asyncio
 
 
 @task
 async def setup_table(block_name: str) -> None:
-    async with await SqlAlchemyConnector.load(block_name) as connector:
+    async with await AsyncSqlAlchemyConnector.load(block_name) as connector:
         await connector.execute(
             "CREATE TABLE IF NOT EXISTS customers (name varchar, address varchar);"
         )
@@ -189,7 +176,7 @@ async def setup_table(block_name: str) -> None:
 @task
 async def fetch_data(block_name: str) -> list:
     all_rows = []
-    async with await SqlAlchemyConnector.load(block_name) as connector:
+    async with await AsyncSqlAlchemyConnector.load(block_name) as connector:
         while True:
             # Repeated fetch* calls using the same operation will
             # skip re-executing and instead return the next set of results

docs/v3/release-notes/index.mdx

@@ -28,13 +28,17 @@ Release notes for Prefect integrations.
 - [prefect-aws](/v3/release-notes/integrations/prefect-aws)
 - [prefect-azure](/v3/release-notes/integrations/prefect-azure)
 - [prefect-bitbucket](/v3/release-notes/integrations/prefect-bitbucket)
+- [prefect-databricks](/v3/release-notes/integrations/prefect-databricks)
 - [prefect-dbt](/v3/release-notes/integrations/prefect-dbt)
 - [prefect-docker](/v3/release-notes/integrations/prefect-docker)
 - [prefect-gcp](/v3/release-notes/integrations/prefect-gcp)
 - [prefect-github](/v3/release-notes/integrations/prefect-github)
 - [prefect-gitlab](/v3/release-notes/integrations/prefect-gitlab)
 - [prefect-kubernetes](/v3/release-notes/integrations/prefect-kubernetes)
 - [prefect-redis](/v3/release-notes/integrations/prefect-redis)
+- [prefect-shell](/v3/release-notes/integrations/prefect-shell)
+- [prefect-snowflake](/v3/release-notes/integrations/prefect-snowflake)
+- [prefect-sqlalchemy](/v3/release-notes/integrations/prefect-sqlalchemy)
 
 
 ## Prefect Cloud