The Andrew thing to me is a bit of a red herring.
(For clarity, I think Andrew is an odious man, so no defending him from me)
The difference is that Harry no longer lives in the country. And he was never without security whilst in this country.
It’s not so much as paying for security, as it seems to be paying for police intel. The police WILL provide security, if they deem there to be a need.
This will be based on their intel, which unfortunately for Harry isn’t for sale.
He can pay for and have private security, he cannot pay for the police to be his private bodyguards if they cannot substantiate it from a police POV.