Detailed arrangements would likely be tax fraud on a tax deductible donation, so I doubt they made such things explicit.

Just because something is called a donation doesn’t mean it qualifies as one.

The amount which is tax-deductible is the amount donated, minus the fair market value of any goods and services and received. If Foo donates $3B for a non-profit hospital in exchange for a promise to slightly bump the priority and treatment Foo and Foo's family, I'd estimate that at least $2.999B of that was tax-deductible. (Is the promise of better treatment worth more than $1M of NPV? I don't think so.)

He donated 200M, the fair market value of priority treatment at a hospital for himself and family via a special phone number for decades could represent a significant fraction of that 200 Million.

Pulling numbers out of a hat, 200k/year * 5 people * 25 years is 25 million. Though the IRS could easily define the fair market value as whatever the minimum donation to receive this level of service.

Sure running the phone number isn’t that expensive, but fair market value of this service is limited by their ability to provide it. They would essentially need to auction off a fixed number of slots per year and in NYC that those slots wouldn’t run cheap.