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

routers/web/explore/topic.go

@@ -0,0 +1,42 @@
+// 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 explore
+
+import (
+	"net/http"
+
+	"code.gitea.io/gitea/models/db"
+	repo_model "code.gitea.io/gitea/models/repo"
+	"code.gitea.io/gitea/modules/context"
+	"code.gitea.io/gitea/modules/convert"
+	api "code.gitea.io/gitea/modules/structs"
+)
+
+// TopicSearch search for creating topic
+func TopicSearch(ctx *context.Context) {
+	opts := &repo_model.FindTopicOptions{
+		Keyword: ctx.FormString("q"),
+		ListOptions: db.ListOptions{
+			Page:     ctx.FormInt("page"),
+			PageSize: convert.ToCorrectPageSize(ctx.FormInt("limit")),
+		},
+	}
+
+	topics, total, err := repo_model.FindTopics(opts)
+	if err != nil {
+		ctx.Error(http.StatusInternalServerError)
+		return
+	}
+
+	topicResponses := make([]*api.TopicResponse, len(topics))
+	for i, topic := range topics {
+		topicResponses[i] = convert.ToTopicResponse(topic)
+	}
+
+	ctx.SetTotalCountHeader(total)
+	ctx.JSON(http.StatusOK, map[string]interface{}{
+		"topics": topicResponses,
+	})
+}