Installing air conditioning in new construction

I retrofitted an air conditioner in the old building and was overjoyed with it until it broke down. The first time it was repaired under warranty, the second time no longer, so not at all, not even at our own expense. The provider is simply garbage. I urgently need a replacement; last summer without air conditioning was hell, and we doubled the walls here with insulation. Still, the warm air comes in when ventilating, and at night it really doesn't cool down. But the new device absolutely must come with a proper warranty; I now place importance on that. By the way: the vulnerable parts are apparently on the circuit board in regulated [Split-Inverter] devices. Instead, you can apparently also use [On-Off] devices, which are switched either off or on, as the name suggests. They are less prone to failure because the electronics are supposedly extremely simple. And an outdoor unit is eliminated. Instead, you have air outlets and a box inside on the wall. I'm still not quite sure if that is something for us. The air conditioning runs for free since we produce the electricity ourselves, meaning plenty of sun = plenty of power. By the way, with our old air conditioner, the condensate water simply ran outside through a hose, without a pump, just with a slope.

. theoretically, it does not have to run constantly but only when there is enough water to pump including collection basin.

That's how it works, nothing runs continuously.

we only want to cool. we neither need heating nor dehumidifying.

That usually comes all at one price because cooling inevitably causes dehumidifying (it's the nature of things). If you then humidify again, you work against the system... so actually pointless.