"But even so, if he’s willing to pay for his paedophile-associating brother’s security himself, why isn’t he willing to pay for his son’s…?"
If Harry was a non-working Royal resident in the UK, then perhaps he would.
We won't know unless/until that happens.
In the mean time, Harry gets security assessments for every trip, and official security will be provided whenever indicated by the risk assessment (remember Harry's case is about having blanket security irrespective of risk assessment, security hasn't been cancelled!)
We also don't know who would foot the bill if Harry needed private security in UK in addition to his own permanent team.
It's entirely reasonable that security arrangements aren't discussed, so we may never know what arrangements are made for Harry.
We only know this about Andrew because of the (long overdue) ending of the tax-payer funded official element (should have gone as soon as he ceased being a working royal). How much he gets and what it really costs going forward might be something the public is curious about, but it's no longer a matter of public interest