As a US citizen, she is only allowed to claim donations to charities registered in the US. The $100k she just dropped in Melbourne, Australia wouldn’t be eligible for example. Therefore it’s not free PR, she actually paid about $100k for it.
A lot of billionaires do donate sums like these without direct personal gain. They also have more complex tax optimization/scams going on. None of that means they are virtuous people, and neither is taylor swift. She's just like any other billionaire.