Ah sorry I thought you planned to break out the floors and pour new ones. Have you checked there is sufficient insulation under the existing floors for UFH to be effective?
FWIW we put in some UFH a couple of years ago, I bought the pipework/manifolds myself from a trade supplier, it came to €1500 for 55sqm of rooms. So I’d say the parts alone for your 160sqm could be €3k. With that in mind and given the work involved in something like this, €9k does not sound expensive to me.