What’s does it mean when it says payment pending? Does that mean it has deposit to TurboTax or pending to my bank account?

Nothing "deposits to TurboTax."  Your refund does not go to TurboTax.  TurboTax does not touch or handle your refund in any way.

You do not say where you are seeing the word "pending".  It would be helpful to know where you see that word.