fix(sync): do not introduce router rebuild timer for full sync (#14001)

* fix(sync): do not introduce router rebuild timer for full sync

* improve code style

* fix comment: remove CP related info

(cherry picked from commit ce668cc)

kong/runloop/handler.lua

@@ -359,12 +359,17 @@ local function new_router(version)
     end
   end
 
-  local detect_changes = kong.core_cache and true
-
-  -- for dbless we will not check changes when initing
-  if db.strategy == "off" and get_phase() == "init_worker" then
-    detect_changes = false
-  end
+  -- We need to detect router changes if there is some one modifying the routers,
+  -- like rebuild_router_timer. And it relies on core_cache to detect changes.
+  --
+  -- 1. stratey off (dbless)
+  --      incremental_sync on:
+  --             non init worker: true(kong.core_cache)
+  --                 init worker: false
+  --      incremental_sync off:   false
+  -- 2. strategy on (non dbless): true(kong.core_cache)
+  local detect_changes = kong.core_cache and
+          (db.strategy ~= "off" or (kong.sync and get_phase() ~= "init_worker"))
 
   local counter = 0
   local page_size = db.routes.pagination.max_page_size
@@ -979,7 +984,10 @@ return {
         end
       end
 
-      do  -- start some rebuild timers
+      -- start some rebuild timers for
+      -- 1. traditional mode
+      -- 2. DP with incremental sync on (dbless mode)
+      if strategy ~= "off" or kong.sync then
         local worker_state_update_frequency = kong.configuration.worker_state_update_frequency or 1
 
         local router_async_opts = {