Add index for last_activity_at order

This benefits the projects API for unauthenticated calls.

Relevant query:

```sql
SELECT
    "projects".*
FROM
    "projects"
WHERE
    "projects"."visibility_level" = 20
    AND "projects"."pending_delete" = FALSE
ORDER BY
    "projects"."last_activity_at" ASC,
    "projects"."id" DESC
LIMIT 20 OFFSET 0
```

Plan without index: https://explain.depesz.com/s/t73N
Plan with index: https://explain.depesz.com/s/V45y

Very similar for the `last_activity_at DESC` sort order.

Relevant issue: https://gitlab.com/gitlab-org/gitlab/issues/36390

Related MR with more explanation:
https://gitlab.com/gitlab-org/gitlab/merge_requests/22623

changelogs/unreleased/ab-projects-api-more-indexes.yml

+---
+title: Add more indexes for other order_by options (Projects API)
+merge_request: 22784
+author:
+type: performance

db/migrate/20200110144316_add_indexes_for_projects_api.rb

+# frozen_string_literal: true
+
+class AddIndexesForProjectsApi < ActiveRecord::Migration[5.2]
+  include Gitlab::Database::MigrationHelpers
+
+  DOWNTIME = false
+
+  disable_ddl_transaction!
+
+  COLUMNS = %i(created_at last_activity_at updated_at name path)
+
+  def up
+    COLUMNS.each do |column|
+      add_concurrent_index :projects, [column, :id], where: 'visibility_level = 20', order: { id: :desc }, name: "index_projects_api_vis20_#{column}_id_desc"
+      add_concurrent_index :projects, [column, :id], where: 'visibility_level = 20', name: "index_projects_api_vis20_#{column}"
+    end
+
+    remove_concurrent_index_by_name :projects, 'index_projects_on_visibility_level_created_at_id_desc'
+    remove_concurrent_index_by_name :projects, 'index_projects_on_visibility_level_created_at_desc_id_desc'
+  end
+
+  def down
+    add_concurrent_index :projects, %i(visibility_level created_at id), order: { id: :desc }, name: 'index_projects_on_visibility_level_created_at_id_desc'
+    add_concurrent_index :projects, %i(visibility_level created_at id), order: { created_at: :desc, id: :desc }, name: 'index_projects_on_visibility_level_created_at_desc_id_desc'
+
+    COLUMNS.each do |column|
+      remove_concurrent_index_by_name :projects, "index_projects_api_vis20_#{column}_id_desc"
+      remove_concurrent_index_by_name :projects, "index_projects_api_vis20_#{column}"
+    end
+  end
+end

db/schema.rb

@@ -10,7 +10,7 @@
 #
 # It's strongly recommended that you check this file into your version control system.
 
-ActiveRecord::Schema.define(version: 2020_01_08_233040) do
+ActiveRecord::Schema.define(version: 2020_01_10_144316) do
 
   # These are extensions that must be enabled in order to support this database
   enable_extension "pg_trgm"
@@ -3353,6 +3353,8 @@ ActiveRecord::Schema.define(version: 2020_01_08_233040) do
     t.boolean "autoclose_referenced_issues"
     t.string "suggestion_commit_message", limit: 255
     t.index "lower((name)::text)", name: "index_projects_on_lower_name"
+    t.index ["created_at", "id"], name: "index_projects_api_vis20_created_at", where: "(visibility_level = 20)"
+    t.index ["created_at", "id"], name: "index_projects_api_vis20_created_at_id_desc", order: { id: :desc }, where: "(visibility_level = 20)"
     t.index ["created_at", "id"], name: "index_projects_on_created_at_and_id"
     t.index ["creator_id"], name: "index_projects_on_creator_id"
     t.index ["description"], name: "index_projects_on_description_trigram", opclass: :gin_trgm_ops, using: :gin
@@ -3360,6 +3362,8 @@ ActiveRecord::Schema.define(version: 2020_01_08_233040) do
     t.index ["id"], name: "index_on_id_partial_with_legacy_storage", where: "((storage_version < 2) OR (storage_version IS NULL))"
     t.index ["id"], name: "index_projects_on_id_partial_for_visibility", unique: true, where: "(visibility_level = ANY (ARRAY[10, 20]))"
     t.index ["id"], name: "index_projects_on_mirror_and_mirror_trigger_builds_both_true", where: "((mirror IS TRUE) AND (mirror_trigger_builds IS TRUE))"
+    t.index ["last_activity_at", "id"], name: "index_projects_api_vis20_last_activity_at", where: "(visibility_level = 20)"
+    t.index ["last_activity_at", "id"], name: "index_projects_api_vis20_last_activity_at_id_desc", order: { id: :desc }, where: "(visibility_level = 20)"
     t.index ["last_activity_at"], name: "index_projects_on_last_activity_at"
     t.index ["last_repository_check_at"], name: "index_projects_on_last_repository_check_at", where: "(last_repository_check_at IS NOT NULL)"
     t.index ["last_repository_check_failed"], name: "index_projects_on_last_repository_check_failed"
@@ -3368,8 +3372,12 @@ ActiveRecord::Schema.define(version: 2020_01_08_233040) do
     t.index ["marked_for_deletion_by_user_id"], name: "index_projects_on_marked_for_deletion_by_user_id", where: "(marked_for_deletion_by_user_id IS NOT NULL)"
     t.index ["mirror_last_successful_update_at"], name: "index_projects_on_mirror_last_successful_update_at"
     t.index ["mirror_user_id"], name: "index_projects_on_mirror_user_id"
+    t.index ["name", "id"], name: "index_projects_api_vis20_name", where: "(visibility_level = 20)"
+    t.index ["name", "id"], name: "index_projects_api_vis20_name_id_desc", order: { id: :desc }, where: "(visibility_level = 20)"
     t.index ["name"], name: "index_projects_on_name_trigram", opclass: :gin_trgm_ops, using: :gin
     t.index ["namespace_id"], name: "index_projects_on_namespace_id"
+    t.index ["path", "id"], name: "index_projects_api_vis20_path", where: "(visibility_level = 20)"
+    t.index ["path", "id"], name: "index_projects_api_vis20_path_id_desc", order: { id: :desc }, where: "(visibility_level = 20)"
     t.index ["path"], name: "index_projects_on_path"
     t.index ["path"], name: "index_projects_on_path_trigram", opclass: :gin_trgm_ops, using: :gin
     t.index ["pending_delete"], name: "index_projects_on_pending_delete"
@@ -3379,8 +3387,8 @@ ActiveRecord::Schema.define(version: 2020_01_08_233040) do
     t.index ["runners_token"], name: "index_projects_on_runners_token"
     t.index ["runners_token_encrypted"], name: "index_projects_on_runners_token_encrypted"
     t.index ["star_count"], name: "index_projects_on_star_count"
-    t.index ["visibility_level", "created_at", "id"], name: "index_projects_on_visibility_level_created_at_desc_id_desc", order: { created_at: :desc, id: :desc }
-    t.index ["visibility_level", "created_at", "id"], name: "index_projects_on_visibility_level_created_at_id_desc", order: { id: :desc }
+    t.index ["updated_at", "id"], name: "index_projects_api_vis20_updated_at", where: "(visibility_level = 20)"
+    t.index ["updated_at", "id"], name: "index_projects_api_vis20_updated_at_id_desc", order: { id: :desc }, where: "(visibility_level = 20)"
   end
 
   create_table "prometheus_alert_events", force: :cascade do |t|