TVs without a tuner are quite popular in Austria. You save around 30€ per month on payments to public TV stations, if your TV is just a monitor and has no tuner.
You can get for example one of those (german, but you probably can read the specs anyway):
Vizio makes (or used to make) those as well. I have one of their 4k 70” without tuner (in the US). It does not suck any less.
Disclaimer: I received it as a “equal replacement” by squaretrade for broken Sharp 70”
Yes, the Rundfunkbeitrag is per household. There are ways to get a reduction, but only because of financial difficulties or a handicap. The devices you own have no effect on the TV tax. It has been so for many years.
Yes, you have to pay the Rundfunkgebühr also if you don't have a TV but your computer has access to the Internet because public broadcasters also have a presence on the Internet.
The functionality is fine. You can turn them on and off. And you probably want to use a soundbar, because of bad speakers. But the panels are just not great. Like all the other TVs in that price range.
You can get for example one of those (german, but you probably can read the specs anyway):
https://nogis.at or https://www.gisbefreit.at/
Most devices are not high end though.