Generally anything you do indoor that falls under normal usage(painting walls, hanging furniture with big screws,etc.) is ok without approval, at least in my country/city(austria) and the land lord can't deny any of this and is not even required to be notified.
As you would have an open window and a not so noise machine running this would be ok, but energy efficiency is quite bad and you lose the benefits of the thermal insulation of your building.
The only thing one needs is a window-sized cardboard with a round hole and blanket if your target room has no door. I just looked at prices and 10000BTU seemed to be ~350 euros.
Doesn't help that in new construction outer walls are usually very well insulated, and inner walls and floors aren't (by design; 70% of total heating cost is evenly split too), so you're working against your neighbors too. We have some stupidly complex building standards often driven by industry lobbying (which also makes building expensive), but installing a mini split hasn't made it on the list.
The real reason most of us don't have AC is because it's hot for a very short period. Last year it definitely wasn't too hot for me to warrant having one. This year so far, it was, for a week: we had about 30°C (86°F) last week, but next week my mobile phone promises it's gonna be 20°C (68°F) maximum, which does not need AC. Maybe that will change, though.
