add daemon.log to the daemon spec (#31273)

* add daemon.log to the daemon spec

* mention use in flutter run --machine
diff --git a/packages/flutter_tools/doc/daemon.md b/packages/flutter_tools/doc/daemon.md
index 1a849b3..4b54e2a 100644
--- a/packages/flutter_tools/doc/daemon.md
+++ b/packages/flutter_tools/doc/daemon.md
@@ -63,10 +63,9 @@
 - `version`: The protocol version. This is the same version returned by the `version()` command.
 - `pid`: The `pid` of the daemon process.
 
-#### daemon.logMessage
+#### daemon.log
 
-The `daemon.logMessage` event is sent whenever a log message is created - either a status level message or an error. The JSON message will contain an `event` field with the value `daemon.logMessage`, and an `params` field containing a map with `level`, `message`, and (optionally) `stackTrace` fields.
-
+This is sent when user-facing output is received. The `params` field will be a map with the field `log`. The `log` field is a string with the output text. If the output indicates an error, an `error` boolean field will be present, and set to `true`.
 
 #### daemon.showMessage
 
@@ -74,6 +73,12 @@
 
 It is up to the client to decide how best to display the message; for some clients, it may map well to a toast style notification. There is an implicit contract that the daemon will not send too many messages over some reasonable period of time.
 
+#### daemon.logMessage
+
+The `daemon.logMessage` event is sent whenever a log message is created - either a status level message or an error. The JSON message will contain an `event` field with the value `daemon.logMessage`, and an `params` field containing a map with `level`, `message`, and (optionally) `stackTrace` fields.
+
+Generally, clients won't display content from `daemon.logMessage` events unless they're set to a more verbose output mode.
+
 ### app domain
 
 #### app.restart
@@ -202,6 +207,7 @@
   - [`shutdown`](#daemonshutdown)
 - Events
   - [`connected`](#daemonconnected)
+  - [`log`](#daemonlog)
   - [`logMessage`](#daemonlogmessage)
 
 ### app domain