Yes nuclear energy is finite.
However, the very same NEA document that optimistically concludes there are 150 years of uranium, also have a graph that shows production will fall short in just 8 years.
https://www.oecd-nea.org/ndd/pubs/2014/7209-uranium-2014.pdf
Note this chart is showing the production shortfall and includes Reasonably Assured Resources RAR because the nuclear industry had to invent their own definition of “Proven Reserves” the rest of the mining industry uses. Why? ask them. Normally new words for the same idea are used for misdirection. This is the situation for real world commercial reactors. Not new unproven tech, not future fantasies. Why do you think there is so much research and money being spent on alternate types of reactors and fuels cycles?
Nuclear power is deadly, dirty, expensive, and short of uranium in 8 years.
It also includes “inferred Resources”
They also make conclusions about how much is available in the future using “Undiscovered resources (prognosticated and speculative)", which I would translate as hopes and dreams.
The problem with these predictions is they fail to include the thermodynamics of mining and refining. At about .01% ore, it takes more energy to mine and refine than the total net energy the nuclear power plants will ever produce.
The end of cheap uranium
Those are from independent sources, not nuclear power PR sources.
The Nuclear Power Regulatory Capture Award:
What’s really fascinating is how every major nuclear agency is chartered to promote nuclear power. Every major nuclear agency is a nuclear power PR agency. The tobacco industry really wishes they could do that.
“The NEA's Mission Statement, as reflected in its Strategic Plan, is:
"To assist its member countries in maintaining and further developing, through international co-operation, the scientific, technological and legal bases required for a safe, environmentally sound and economical use of nuclear energy for peaceful purposes. It strives to provide authoritative assessments and to forge common understandings on key issues as input to government decisions on nuclear energy policy and to broader OECD analyses in areas such as energy and the sustainable development of low-carbon economies."
IAEA:
“ARTICLE II: Objectives
The Agency shall seek to accelerate and enlarge the contribution of atomic energy to peace, health and prosperity throughout the world. It shall ensure, so far as it is able, that assistance provided by it or at its request or under its supervision or control is not used in such a way as to further any military purpose.”
However, there is plenty of uranium for the level of nuclear power in the world today, ~12%.
If we implemented enough nuclear power to supplement renewables and end most use of fossil fuels (~33% of all electricity generation worldwide), we would need to employ some new technologies.
Fast-spectrum nuclear reactors can reuse nuclear fuel via reprocessesing. It is a challenging technology, but it has been implemented in the past on a smaller scale. Some advanced next-gen reactors can use their fuel very efficiently, like the “traveling -wave” reactor from TerraPower.