chore(tornado): drop support for <6.1 (#15369)

## Description

Drops support for Tornado versions less than 6.1. The minimum supported
version is now Tornado >=6.1, which is asyncio-based. Updated tests and
documentation to reflect this change.

## Testing

Updated Tornado integration tests to only run against Tornado >=6.1. All
existing tests pass with the new minimum version requirement.

## Risks

Low. Tornado v6.1 was released in 2020 and has been stable. Users on
older versions will need to upgrade to continue using the integration.

## Additional Notes

- Updated `_supported_versions()` to reflect the new minimum version
requirement
- Updated documentation to specify Tornado >=6.1 support
- Updated test matrix in `riotfile.py` to remove older Tornado versions

Author: mabdinur

.riot/requirements/1099f43.txt

@@ -2,10 +2,10 @@
 # This file is autogenerated by pip-compile with Python 3.9
 # by the following command:
 #
-#    pip-compile --allow-unsafe --no-annotate --resolver=backtracking .riot/requirements/aaa8f63.in
+#    pip-compile --allow-unsafe --no-annotate .riot/requirements/1da9e5b.in
 #
-attrs==25.3.0
-coverage[toml]==7.8.2
+attrs==25.4.0
+coverage[toml]==7.10.7
 exceptiongroup==1.3.0
 hypothesis==6.45.0
 importlib-metadata==8.7.0
@@ -15,11 +15,11 @@ opentracing==2.4.0
 packaging==25.0
 pluggy==1.6.0
 pytest==8.0.0
-pytest-cov==6.1.1
-pytest-mock==3.14.1
-pytest-randomly==3.16.0
+pytest-cov==7.0.0
+pytest-mock==3.15.1
+pytest-randomly==4.0.1
 sortedcontainers==2.4.0
-tomli==2.2.1
-tornado==6.0.4
-typing-extensions==4.14.0
+tomli==2.3.0
+tornado==6.1
+typing-extensions==4.15.0
 zipp==3.23.0

.riot/requirements/116a9e0.txt

@@ -874,7 +874,7 @@ integrations:
   - tornado
   tested_versions_by_dependency:
     tornado:
-      min: 6.0.4
+      min: "6.1"
       max: 6.5.1
 
 - integration_name: unittest

.riot/requirements/17298d6.txt

@@ -0,0 +1,99 @@
+r"""
+The Tornado integration traces all ``RequestHandler`` defined in a Tornado web application.
+Auto instrumentation is available using the ``patch`` function that **must be called before**
+importing the tornado library.
+
+This integration supports Tornado >=6.1, which is asyncio-based. The integration properly
+handles async/await coroutines and functions that return Futures, ensuring accurate span
+durations and correct context propagation.
+
+The following is an example::
+
+    # patch before importing tornado and concurrent.futures
+    import asyncio
+    import tornado.web
+    import tornado.httpserver
+
+    class MainHandler(tornado.web.RequestHandler):
+        def get(self):
+            self.write("Hello, world")
+
+    async def main():
+        app = tornado.web.Application([
+            (r"/", MainHandler),
+        ])
+        server = tornado.httpserver.HTTPServer(app)
+        server.listen(8888)
+
+        # Let the asyncio loop run forever
+        await asyncio.Event().wait()
+
+    if __name__ == "__main__":
+        asyncio.run(main())
+
+When any type of ``RequestHandler`` is hit, a request root span is automatically created. If
+you want to trace more parts of your application, you can use the ``wrap()`` decorator and
+the ``trace()`` method as usual::
+
+    class MainHandler(tornado.web.RequestHandler):
+        async def get(self):
+            await self.notify()
+            await self.blocking_method()
+            with tracer.trace('tornado.before_write') as span:
+                # trace more work in the handler
+
+        @tracer.wrap('tornado.executor_handler')
+        @tornado.concurrent.run_on_executor
+        def blocking_method(self):
+            # do something expensive
+
+        @tracer.wrap('tornado.notify', service='tornado-notification')
+        async def notify(self):
+            # do something
+
+If you are overriding the ``on_finish`` or ``log_exception`` methods on a
+``RequestHandler``, you will need to call the super method to ensure the
+tracer's patched methods are called::
+
+    class MainHandler(tornado.web.RequestHandler):
+        async def get(self):
+            self.write("Hello, world")
+
+        def on_finish(self):
+            super(MainHandler, self).on_finish()
+            # do other clean-up
+
+        def log_exception(self, typ, value, tb):
+            super(MainHandler, self).log_exception(typ, value, tb)
+            # do other logging
+
+Tornado settings can be used to change some tracing configuration, like::
+
+    settings = {
+        'datadog_trace': {
+            'default_service': 'my-tornado-app',
+            'tags': {'env': 'production'},
+            'distributed_tracing': False,
+        },
+    }
+
+    app = tornado.web.Application([
+        (r'/', MainHandler),
+    ], **settings)
+
+The available settings are:
+
+* ``default_service`` (default: `tornado-web`): set the service name used by the tracer. Usually
+  this configuration must be updated with a meaningful name. Can also be configured via the
+  ``DD_SERVICE`` environment variable.
+* ``tags`` (default: `{}`): set global tags that should be applied to all spans.
+* ``enabled`` (default: `True`): define if the tracer is enabled or not. If set to `false`, the
+  code is still instrumented but no spans are sent to the APM agent.
+* ``distributed_tracing`` (default: `None`): enable distributed tracing if this is called
+  remotely from an instrumented application. Overrides the integration config which is configured via the
+  ``DD_TORNADO_DISTRIBUTED_TRACING`` environment variable.
+  We suggest to enable it only for internal services where headers are under your control.
+* ``agent_hostname`` (default: `localhost`): define the hostname of the APM agent.
+* ``agent_port`` (default: `8126`): define the port of the APM agent.
+* ``settings`` (default: ``{}``): Tracer extra settings used to change, for instance, the filtering behavior.
+"""

.riot/requirements/18f2a74.txt

@@ -44,7 +44,7 @@ def get_version():
 
 
 def _supported_versions() -> Dict[str, str]:
-    return {"tornado": ">=6.0.0"}
+    return {"tornado": ">=6.1"}
 
 
 def patch():