Google raising price of YouTube Premium to $13.99 per month

Is it just a case of Google’s costs going up or simply their need to make more profit to delight shareholders?

Yes. Everyone else is raising their prices due to "increased costs", even if they don't actually have any increased costs, because it's a "get out of jail free" card for raising your costs at the moment. Everyone is doing it, so you're less likely to get negative media coverage if you do it as well.