[API] add GET /orgs endpoint (#9560)

* introduce `GET /orgs`

* add TEST

* show also other VisibleType's

* update description

* refactor a lot

* SearchUserOptions by default return only public

routers/admin/orgs.go

@@ -9,6 +9,7 @@ import (
 	"code.gitea.io/gitea/modules/base"
 	"code.gitea.io/gitea/modules/context"
 	"code.gitea.io/gitea/modules/setting"
+	"code.gitea.io/gitea/modules/structs"
 	"code.gitea.io/gitea/routers"
 )
 
@@ -25,6 +26,6 @@ func Organizations(ctx *context.Context) {
 	routers.RenderUserSearch(ctx, &models.SearchUserOptions{
 		Type:     models.UserTypeOrganization,
 		PageSize: setting.UI.Admin.OrgPagingNum,
-		Private:  true,
+		Visible:  []structs.VisibleType{structs.VisibleTypePublic, structs.VisibleTypeLimited, structs.VisibleTypePrivate},
 	}, tplOrgs)
 }