Okay, so taking into account that it is an utterly dysfunctional organisation they can deliver some services well. That certainly doesn't mean they are doing a good job. That means that they deliver some good services. That's two completely different things.
Your GP got paid €33 per shot for the Covid jab and €11 per shot for the Flu jab (€30 plus a €10% pension contribution and €10 plus a €10% pension contribution). So it wasn't free, it cost the State €143, plus the cost of the vaccines, plus their internal procurement and administration cost to give you those injections. The total is probably well north of €200.