tpl: Fix incorrect template selection order

tpl/tplimpl/templatestore.go

@@ -1212,6 +1212,12 @@ func (s *TemplateStore) insertTemplate2(
 		replace = subCategory == SubCategoryInline && nkExisting.subCategory == SubCategoryInline
 	}
 
+	if !replace && existingFound && fi != nil && nkExisting.Fi != nil {
+		// Fix issue #13877.
+		primarySuffix := s.htmlFormat.MediaType.FirstSuffix.FullSuffix
+		replace = strings.HasSuffix(fi.Name(), primarySuffix) && !strings.HasSuffix(nkExisting.Fi.Name(), primarySuffix)
+	}
+
 	if !replace && existingFound {
 		if len(pi.Identifiers()) >= len(nkExisting.PathInfo.Identifiers()) {
 			// e.g. /pages/home.foo.html and  /pages/home.html where foo may be a valid language name in another site.

tpl/tplimpl/templatestore_test.go

@@ -0,0 +1,38 @@
+package tplimpl_test
+
+import (
+	"testing"
+
+	"github.com/gohugoio/hugo/hugolib"
+)
+
+func TestIssue13877(t *testing.T) {
+	t.Parallel()
+
+	files := `
+-- hugo.toml --
+disableKinds = ['home','rss','section','sitemap','taxonomy','term']
+
+[mediaTypes.'text/html']
+suffixes = ['b','a','d','c']
+
+[outputFormats.html]
+mediaType = 'text/html'
+-- content/p1.md --
+---
+title: p1
+---
+-- layouts/page.html.a --
+{{ templates.Current.Name }}
+-- layouts/page.html.b --
+{{ templates.Current.Name }}
+-- layouts/page.html.c --
+{{ templates.Current.Name }}
+-- layouts/page.html.d --
+{{ templates.Current.Name }}
+`
+
+	b := hugolib.Test(t, files)
+
+	b.AssertFileContent("public/p1/index.b", "page.html.b")
+}