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/repo/repo.go

@@ -20,11 +20,14 @@ import (
 	user_model "code.gitea.io/gitea/models/user"
 	"code.gitea.io/gitea/modules/base"
 	"code.gitea.io/gitea/modules/context"
+	"code.gitea.io/gitea/modules/convert"
 	"code.gitea.io/gitea/modules/graceful"
 	"code.gitea.io/gitea/modules/log"
 	repo_module "code.gitea.io/gitea/modules/repository"
 	"code.gitea.io/gitea/modules/setting"
 	"code.gitea.io/gitea/modules/storage"
+	api "code.gitea.io/gitea/modules/structs"
+	"code.gitea.io/gitea/modules/util"
 	"code.gitea.io/gitea/modules/web"
 	"code.gitea.io/gitea/services/forms"
 	repo_service "code.gitea.io/gitea/services/repository"
@@ -503,3 +506,112 @@ func InitiateDownload(ctx *context.Context) {
 		"complete": completed,
 	})
 }
+
+// SearchRepo repositories via options
+func SearchRepo(ctx *context.Context) {
+	opts := &models.SearchRepoOptions{
+		ListOptions: db.ListOptions{
+			Page:     ctx.FormInt("page"),
+			PageSize: convert.ToCorrectPageSize(ctx.FormInt("limit")),
+		},
+		Actor:              ctx.Doer,
+		Keyword:            ctx.FormTrim("q"),
+		OwnerID:            ctx.FormInt64("uid"),
+		PriorityOwnerID:    ctx.FormInt64("priority_owner_id"),
+		TeamID:             ctx.FormInt64("team_id"),
+		TopicOnly:          ctx.FormBool("topic"),
+		Collaborate:        util.OptionalBoolNone,
+		Private:            ctx.IsSigned && (ctx.FormString("private") == "" || ctx.FormBool("private")),
+		Template:           util.OptionalBoolNone,
+		StarredByID:        ctx.FormInt64("starredBy"),
+		IncludeDescription: ctx.FormBool("includeDesc"),
+	}
+
+	if ctx.FormString("template") != "" {
+		opts.Template = util.OptionalBoolOf(ctx.FormBool("template"))
+	}
+
+	if ctx.FormBool("exclusive") {
+		opts.Collaborate = util.OptionalBoolFalse
+	}
+
+	mode := ctx.FormString("mode")
+	switch mode {
+	case "source":
+		opts.Fork = util.OptionalBoolFalse
+		opts.Mirror = util.OptionalBoolFalse
+	case "fork":
+		opts.Fork = util.OptionalBoolTrue
+	case "mirror":
+		opts.Mirror = util.OptionalBoolTrue
+	case "collaborative":
+		opts.Mirror = util.OptionalBoolFalse
+		opts.Collaborate = util.OptionalBoolTrue
+	case "":
+	default:
+		ctx.Error(http.StatusUnprocessableEntity, fmt.Sprintf("Invalid search mode: \"%s\"", mode))
+		return
+	}
+
+	if ctx.FormString("archived") != "" {
+		opts.Archived = util.OptionalBoolOf(ctx.FormBool("archived"))
+	}
+
+	if ctx.FormString("is_private") != "" {
+		opts.IsPrivate = util.OptionalBoolOf(ctx.FormBool("is_private"))
+	}
+
+	sortMode := ctx.FormString("sort")
+	if len(sortMode) > 0 {
+		sortOrder := ctx.FormString("order")
+		if len(sortOrder) == 0 {
+			sortOrder = "asc"
+		}
+		if searchModeMap, ok := context.SearchOrderByMap[sortOrder]; ok {
+			if orderBy, ok := searchModeMap[sortMode]; ok {
+				opts.OrderBy = orderBy
+			} else {
+				ctx.Error(http.StatusUnprocessableEntity, fmt.Sprintf("Invalid sort mode: \"%s\"", sortMode))
+				return
+			}
+		} else {
+			ctx.Error(http.StatusUnprocessableEntity, fmt.Sprintf("Invalid sort order: \"%s\"", sortOrder))
+			return
+		}
+	}
+
+	var err error
+	repos, count, err := models.SearchRepository(opts)
+	if err != nil {
+		ctx.JSON(http.StatusInternalServerError, api.SearchError{
+			OK:    false,
+			Error: err.Error(),
+		})
+		return
+	}
+
+	results := make([]*api.Repository, len(repos))
+	for i, repo := range repos {
+		if err = repo.GetOwner(ctx); err != nil {
+			ctx.JSON(http.StatusInternalServerError, api.SearchError{
+				OK:    false,
+				Error: err.Error(),
+			})
+			return
+		}
+		accessMode, err := models.AccessLevel(ctx.Doer, repo)
+		if err != nil {
+			ctx.JSON(http.StatusInternalServerError, api.SearchError{
+				OK:    false,
+				Error: err.Error(),
+			})
+		}
+		results[i] = convert.ToRepo(repo, accessMode)
+	}
+
+	ctx.SetTotalCountHeader(count)
+	ctx.JSON(http.StatusOK, api.SearchResults{
+		OK:   true,
+		Data: results,
+	})
+}