How long does it have to last to qualify?
There will of course be scope for arguments: should it be the highest structure, tallest occupied building, highest occupied floor,
And the less glamorous sides: slowest lift, most alarming swaying in winds or earthquakes, highest floor you can be rescued from, highest floor where water pressure is adequate.
But it does sound like the kind of that could have taken off, and you'd get additional competition from eg China, rich oil states.
345m tall statue of Chairman Mao, 347m minaret in Brunei etc. Shame I lack the drawing skills to sketch these out.