Wording improvements for the TaskScheduler (#17992)

As I found the current docstrings a bit unclear while trying to wrap my
head around this class.

changelog.d/17992.doc

@@ -0,0 +1 @@
+Improve documentation for the `TaskScheduler` class.

synapse/util/task_scheduler.py

@@ -46,33 +46,43 @@
 
 class TaskScheduler:
     """
-    This is a simple task sheduler aimed at resumable tasks: usually we use `run_in_background`
-    to launch a background task, or Twisted `deferLater` if we want to do so later on.
-
-    The problem with that is that the tasks will just stop and never be resumed if synapse
-    is stopped for whatever reason.
-
-    How this works:
-    - A function mapped to a named action should first be registered with `register_action`.
-    This function will be called when trying to resuming tasks after a synapse shutdown,
-    so this registration should happen when synapse is initialised, NOT right before scheduling
-    a task.
-    - A task can then be launched using this named action with `schedule_task`. A `params` dict
-    can be passed, and it will be available to the registered function when launched. This task
-    can be launch either now-ish, or later on by giving a `timestamp` parameter.
-
-    The function may call `update_task` at any time to update the `result` of the task,
-    and this can be used to resume the task at a specific point and/or to convey a result to
-    the code launching the task.
-    You can also specify the `result` (and/or an `error`) when returning from the function.
-
-    The reconciliation loop runs every minute, so this is not a precise scheduler.
-    There is a limit of 10 concurrent tasks, so tasks may be delayed if the pool is already
-    full. In this regard, please take great care that scheduled tasks can actually finished.
-    For now there is no mechanism to stop a running task if it is stuck.
-
-    Tasks will be run on the worker specified with `run_background_tasks_on` config,
-    or the main one by default.
+    This is a simple task scheduler designed for resumable tasks. Normally,
+    you'd use `run_in_background` to start a background task or Twisted's
+    `deferLater` if you want to run it later.
+
+    The issue is that these tasks stop completely and won't resume if Synapse is
+    shut down for any reason.
+
+    Here's how it works:
+
+    - Register an Action: First, you need to register a function to a named
+      action using `register_action`. This function will be called to resume tasks
+      after a Synapse shutdown. Make sure to register it when Synapse initializes,
+      not right before scheduling the task.
+
+    - Schedule a Task: You can launch a task linked to the named action
+      using `schedule_task`. You can pass a `params` dictionary, which will be
+      passed to the registered function when it's executed. Tasks can be scheduled
+      to run either immediately or later by specifying a `timestamp`.
+
+    - Update Task: The function handling the task can call `update_task` at
+      any point to update the task's `result`. This lets you resume the task from
+      a specific point or pass results back to the code that scheduled it. When
+      the function completes, you can also return a `result` or an `error`.
+
+    Things to keep in mind:
+
+    - The reconciliation loop runs every minute, so this is not a high-precision
+      scheduler.
+
+    - Only 10 tasks can run at the same time. If the pool is full, tasks may be
+      delayed. Make sure your scheduled tasks can actually finish.
+
+    - Currently, there's no way to stop a task if it gets stuck.
+
+    - Tasks will run on the worker defined by the `run_background_tasks_on`
+      setting in your configuration. If no worker is specified, they'll run on
+      the main one by default.
     """
 
     # Precision of the scheduler, evaluation of tasks to run will only happen
@@ -157,7 +167,7 @@ async def schedule_task(
         params: Optional[JsonMapping] = None,
     ) -> str:
         """Schedule a new potentially resumable task. A function matching the specified
-        `action` should have be registered with `register_action` before the task is run.
+        `action` should've been registered with `register_action` before the task is run.
 
         Args:
             action: the name of a previously registered action
@@ -210,22 +220,28 @@ async def update_task(
         result: Optional[JsonMapping] = None,
         error: Optional[str] = None,
     ) -> bool:
-        """Update some task associated values. This is exposed publicly so it can
-        be used inside task functions, mainly to update the result and be able to
-        resume a task at a specific step after a restart of synapse.
+        """Update some task-associated values. This is exposed publicly so it can
+        be used inside task functions, mainly to update the result or resume
+        a task at a specific step after a restart of synapse.
 
         It can also be used to stage a task, by setting the `status` to `SCHEDULED` with
         a new timestamp.
 
-        The `status` can only be set to `ACTIVE` or `SCHEDULED`, `COMPLETE` and `FAILED`
-        are terminal status and can only be set by returning it in the function.
+        The `status` can only be set to `ACTIVE` or `SCHEDULED`. `COMPLETE` and `FAILED`
+        are terminal statuses and can only be set by returning them from the function.
 
         Args:
             id: the id of the task to update
             timestamp: useful to schedule a new stage of the task at a later date
             status: the new `TaskStatus` of the task
             result: the new result of the task
             error: the new error of the task
+
+        Returns:
+            True if the update was successful, False otherwise.
+
+        Raises:
+            Exception: If a status other than `ACTIVE` or `SCHEDULED` was passed.
         """
         if status == TaskStatus.COMPLETE or status == TaskStatus.FAILED:
             raise Exception(
@@ -263,9 +279,9 @@ async def get_tasks(
         max_timestamp: Optional[int] = None,
         limit: Optional[int] = None,
     ) -> List[ScheduledTask]:
-        """Get a list of tasks. Returns all the tasks if no args is provided.
+        """Get a list of tasks. Returns all the tasks if no args are provided.
 
-        If an arg is `None` all tasks matching the other args will be selected.
+        If an arg is `None`, all tasks matching the other args will be selected.
         If an arg is an empty list, the corresponding value of the task needs
         to be `None` to be selected.
 
@@ -277,8 +293,8 @@ async def get_tasks(
                 a timestamp inferior to the specified one
             limit: Only return `limit` number of rows if set.
 
-        Returns
-            A list of `ScheduledTask`, ordered by increasing timestamps
+        Returns:
+            A list of `ScheduledTask`, ordered by increasing timestamps.
         """
         return await self._store.get_scheduled_tasks(
             actions=actions,