Fix rebuilds when running hugo -w

This was partly broken in Hugo 0.123.0.

We have two internal config options that gets set from the CLI:

* Running; a web server is running
* Watching; either set via `hugo -w`  or `hugo server --watch=false`

Part of the change detection code wrongly used the `Running` as a flag when `Watching` would be the correct.

Fixes #12296

hugolib/integrationtest_builder.go

@@ -38,12 +38,20 @@ import (
 
 type TestOpt func(*IntegrationTestConfig)
 
+// TestOptRunning will enable running in integration tests.
 func TestOptRunning() TestOpt {
 	return func(c *IntegrationTestConfig) {
 		c.Running = true
 	}
 }
 
+// TestOptWatching will enable watching in integration tests.
+func TestOptWatching() TestOpt {
+	return func(c *IntegrationTestConfig) {
+		c.Watching = true
+	}
+}
+
 // Enable tracing in integration tests.
 // THis should only be used during development and not committed to the repo.
 func TestOptTrace() TestOpt {
@@ -570,6 +578,10 @@ func (s *IntegrationTestBuilder) initBuilder() error {
 				"running": s.Cfg.Running,
 				"watch":   s.Cfg.Running,
 			})
+		} else if s.Cfg.Watching {
+			flags.Set("internal", maps.Params{
+				"watch": s.Cfg.Watching,
+			})
 		}
 
 		if s.Cfg.WorkingDir != "" {
@@ -817,6 +829,11 @@ type IntegrationTestConfig struct {
 	// Whether to simulate server mode.
 	Running bool
 
+	// Watch for changes.
+	// This is (currently) always set to true when Running is set.
+	// Note that the CLI for the server does allow for --watch=false, but that is not used in these test.
+	Watching bool
+
 	// Will print the log buffer after the build
 	Verbose bool