This is the async-ready almost-equivalent of Monitor. It's only almost equivalent because the Monitor type permits reentrancy, which is not currently possible to do with an async-ready lock.
An AsyncMonitor is an AsyncLock with a single associated AsyncConditionVariable. It is either entered or not. The AsyncMonitor can be asynchronously entered by calling EnterAsync, and you can leave it by disposing the result of that task.
While in the monitor, a task may decide to wait for a signal by calling WaitAsync. While waiting, it temporarily leaves the monitor until it receives a signal and re-enters the monitor.
While in the monitor, a signalling task may choose to release only a single waiter (Pulse) or all waiters (PulseAll). If there are no waiters, the notification is "lost"; it is not remembered by the AsyncMonitor.
The task returned from EnterAsync will enter the Completed state when it has entered the monitor. That same task will enter the Canceled state if the CancellationToken is signaled before the wait is satisfied; in that case, the monitor is not entered by that task.
The task returned from WaitAsync will enter the Completed state when it receives a signal and re-enters the monitor. That same task will enter the Canceled state if the CancellationToken is signaled before the wait is satisfied; in that case, the task will wait to enter the Canceled state until it re-enters the monitor.
Remember that from the time WaitAsync is called to the time when its returned task completes, the calling task has left the monitor.
Note that the correct logic for waiting on monitor signals is to wait in a loop until the required condition is true. This is necessary because other tasks may execute between the signal and the completion of the wait.
You can call EnterAsync with an already-cancelled CancellationToken to attempt to enter the monitor immediately without actually entering the wait queue.