First section your Article: "As of 2017, identified uranium reserves recoverable at US$130/kg were 6.14 million tons (compared to 5.72 million tons in 2015). At the rate of consumption in 2017, these reserves are sufficient for slightly over 130 years of supply. The identified reserves as of 2017 recoverable at US$260/kg are 7.99 million tons (compared to 7.64 million tons in 2015).[9]"

Doesn't seem clearcut

No, these are the reserve that are available at a given price. It is very sensitive to technology. Moreover, price of uranium is a small part of the cost of a powerplant, so there is not as much price sensitivity. We're still good for around ~200 years.

Also, fuel can be reprocessed, and we can use other things than Uranium

Almost all predictions of running out of ores have been wrong. They’re based on “proven reserves,” but mining companies don’t bother proving much beyond 50 years worth.

I wouldn't worry too much about running out of nuclear fuel. There's also Pu used in MOX fuel, breeder reactors, nuclear fuel reprocessing.