I don’t know how angel flight works but if there is no payment to the pilot owner by the passengers in any way, then no it doesn’t meet the definition of AT.
The reg was always worded that a pilot may not receive remuneration from any party for the flight in question, passenger or completely unrelated entity. Unless of course you fulfilled the cost sharing requirements. The point is whether you receive payment or reward directly for the flight operation.
You could get around that by being paid as an employee of a company for something else and conduct the flight for free in a certain way, or the company pays all costs for its aircraft etc...