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

web_src/js/features/repo-template.js

@@ -23,7 +23,7 @@ export function initRepoTemplateSearch() {
     $('#repo_template_search')
       .dropdown({
         apiSettings: {
-          url: `${appSubUrl}/api/v1/repos/search?q={query}&template=true&priority_owner_id=${$('#uid').val()}`,
+          url: `${appSubUrl}/repo/search?q={query}&template=true&priority_owner_id=${$('#uid').val()}`,
           onResponse(response) {
             const filteredResponse = {success: true, results: []};
             filteredResponse.results.push({