The other group the article references, the Polar Bear Specialist Group, sadly isn't much better than the GWPF.

Look at their most recent report, they show "Data deficient" for most subpopulations. I think the other comment is likely correct, the population is going up, but for reasons unrelated to the existence of global warming. https://www.iucn-pbsg.org/

This doesn't fit the environmentalist narrative well, so the most prominent statistics on their homepage aren't directly related to polar bear populations, but things like "The mean rate of decline in summer sea ice area across all subpopulations "

>Of the 19 polar bear subpopulations recognized in 2017, one was in decline, two were increasing, seven were stable, and nine had insufficient data.[48]

https://web.archive.org/web/20151224224314/http://pbsg.npola...

It seems a multispectral satellite photo would quite easily spot bears. Heat signature visible in the IR, and shadow in the visible spectrum.

You could get pretty good population estimates by just reviewing random 1 km^2 samples for bears and then extrapolating.