Reimplement and simplify Hugo's template system

See #13541 for details.

Fixes #13545
Fixes #13515
Closes #7964
Closes #13365
Closes #12988
Closes #4891

tpl/templates/defer_integration_test.go

@@ -71,6 +71,81 @@ AMP.
 
 `
 
+func TestDeferNoBaseof(t *testing.T) {
+	t.Parallel()
+
+	files := `
+-- hugo.toml --
+-- layouts/index.html --
+Home.
+{{ with (templates.Defer (dict "key" "foo")) }}
+ Defer
+{{ end }}
+-- content/_index.md --
+---
+title: "Home"
+---
+
+`
+
+	b := hugolib.Test(t, files)
+
+	b.AssertFileContent("public/index.html", "Home.\n\n Defer")
+}
+
+func TestDeferBaseof(t *testing.T) {
+	t.Parallel()
+
+	files := `
+-- hugo.toml --
+-- layouts/baseof.html --
+{{ with (templates.Defer (dict "key" "foo")) }}
+Defer
+{{ end }}
+Block:{{ block "main" . }}{{ end }}$
+-- layouts/index.html --
+{{ define "main" }}
+Home.
+{{ end }}
+-- content/_index.md --
+---
+title: "Home"
+---
+
+`
+
+	b := hugolib.Test(t, files)
+
+	b.AssertFileContent("public/index.html", "Home.\n\n Defer")
+}
+
+func TestDeferMain(t *testing.T) {
+	t.Parallel()
+
+	files := `
+-- hugo.toml --
+-- layouts/baseof.html --
+
+Block:{{ block "main" . }}{{ end }}$
+-- layouts/index.html --
+{{ define "main" }}
+Home.
+{{ with (templates.Defer (dict "key" "foo")) }}
+Defer
+{{ end }}
+{{ end }}
+-- content/_index.md --
+---
+title: "Home"
+---
+
+`
+
+	b := hugolib.Test(t, files)
+
+	b.AssertFileContent("public/index.html", "Home.\n\n Defer")
+}
+
 func TestDeferBasic(t *testing.T) {
 	t.Parallel()
 

tpl/templates/templates.go

@@ -44,7 +44,7 @@ type Namespace struct {
 // Note that this is the Unix-styled relative path including filename suffix,
 // e.g. partials/header.html
 func (ns *Namespace) Exists(name string) bool {
-	return ns.deps.Tmpl().HasTemplate(name)
+	return ns.deps.GetTemplateStore().HasTemplate(name)
 }
 
 // Defer defers the execution of a template block.
@@ -93,7 +93,7 @@ func (ns *Namespace) DoDefer(ctx context.Context, id string, optsv any) string {
 	_, _ = ns.deps.BuildState.DeferredExecutions.Executions.GetOrCreate(id,
 		func() (*tpl.DeferredExecution, error) {
 			return &tpl.DeferredExecution{
-				TemplateName: templateName,
+				TemplatePath: templateName,
 				Ctx:          ctx,
 				Data:         opts.Data,
 				Executed:     false,