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/user/stop_watch.go

@@ -0,0 +1,41 @@
+// 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 user
+
+import (
+	"net/http"
+
+	"code.gitea.io/gitea/models"
+	"code.gitea.io/gitea/models/db"
+	"code.gitea.io/gitea/modules/context"
+	"code.gitea.io/gitea/modules/convert"
+)
+
+// GetStopwatches get all stopwatches
+func GetStopwatches(ctx *context.Context) {
+	sws, err := models.GetUserStopwatches(ctx.Doer.ID, db.ListOptions{
+		Page:     ctx.FormInt("page"),
+		PageSize: convert.ToCorrectPageSize(ctx.FormInt("limit")),
+	})
+	if err != nil {
+		ctx.Error(http.StatusInternalServerError, err.Error())
+		return
+	}
+
+	count, err := models.CountUserStopwatches(ctx.Doer.ID)
+	if err != nil {
+		ctx.Error(http.StatusInternalServerError, err.Error())
+		return
+	}
+
+	apiSWs, err := convert.ToStopWatches(sws)
+	if err != nil {
+		ctx.Error(http.StatusInternalServerError, err.Error())
+		return
+	}
+
+	ctx.SetTotalCountHeader(count)
+	ctx.JSON(http.StatusOK, apiSWs)
+}