"從h4轉到h1b雖然是新的h1,也不用占用那些每年新的h1
b名額吧"
This is correct.
You should apply h4. When you apply new h1b, you cannot work until the new h1b is approved, it's not related to the quota however. For your GC application, the priority date for your previous application is valid if your new employer would apply GC for you.