Never use /api/v1 from Gitea UI Pages (#19318)

Reusing `/api/v1` from Gitea UI Pages have pros and cons.
Pros:
1) Less code copy

Cons:
1) API/v1 have to support shared session with page requests.
2) You need to consider for each other when you want to change something about api/v1 or page.

This PR moves all dependencies to API/v1 from UI Pages.

Partially replace #16052

integrations/repo_topic_test.go

@@ -0,0 +1,46 @@
+// Copyright 2022 The Gitea Authors. All rights reserved.
+// Use of this source code is governed by a MIT-style
+// license that can be found in the LICENSE file.
+
+package integrations
+
+import (
+	"net/http"
+	"net/url"
+	"testing"
+
+	api "code.gitea.io/gitea/modules/structs"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestTopicSearch(t *testing.T) {
+	defer prepareTestEnv(t)()
+	searchURL, _ := url.Parse("/explore/topics/search")
+	var topics struct {
+		TopicNames []*api.TopicResponse `json:"topics"`
+	}
+
+	query := url.Values{"page": []string{"1"}, "limit": []string{"4"}}
+
+	searchURL.RawQuery = query.Encode()
+	res := MakeRequest(t, NewRequest(t, "GET", searchURL.String()), http.StatusOK)
+	DecodeJSON(t, res, &topics)
+	assert.Len(t, topics.TopicNames, 4)
+	assert.EqualValues(t, "6", res.Header().Get("x-total-count"))
+
+	query.Add("q", "topic")
+	searchURL.RawQuery = query.Encode()
+	res = MakeRequest(t, NewRequest(t, "GET", searchURL.String()), http.StatusOK)
+	DecodeJSON(t, res, &topics)
+	assert.Len(t, topics.TopicNames, 2)
+
+	query.Set("q", "database")
+	searchURL.RawQuery = query.Encode()
+	res = MakeRequest(t, NewRequest(t, "GET", searchURL.String()), http.StatusOK)
+	DecodeJSON(t, res, &topics)
+	if assert.Len(t, topics.TopicNames, 1) {
+		assert.EqualValues(t, 2, topics.TopicNames[0].ID)
+		assert.EqualValues(t, "database", topics.TopicNames[0].Name)
+		assert.EqualValues(t, 1, topics.TopicNames[0].RepoCount)
+	}
+}