Sustainable? What do you count as sustainable? Do you consider for example solar power or wind power or geothermal power sustainable?
They aren't. If you extract solar power, eventually the sun has run out of fusion fuel, and you can't extract solar power anymore. Same for wind -- it's just harvesting solar power in an indirect way. Geothermal power relies on earth having enough thermal energy. The faster you extract geothermal heat energy, the faster it runs out.
However, if we bend a little bit the definition of "sustainability", and consider solutions that have enough fuel for 5 billion years "sustainable", then some forms of nuclear energy are sustainable. Nuclear energy based on U-235 isn't (as only 0.7% of natural uranium is U-235, so eventually we will run out of U-235 and have only U-238 left), but nuclear energy based on U-238 (converting it to plutonium in breeder reactors) is sustainable. Also, thorium reactors are sustainable too (they convert thorium to U-233) because essentially all of thorium is the isotope 232, and it can be converted entirely to U-233 in breeder reactors.
Also good breeder reactors that have proper waste processing (a lot of the waste, especially of the most active waste, is good nuclear fuel) can provide a waste stream that decays faster than the waste stream of our once-through reactors. So the waste issue is mostly solved, because only 300-400 years of storage is needed for the waste (it decays in 300-400 years to the activity of natural ore) as opposed to hundreds of thousands or millions of years of the waste of current reactors.
Current nuclear reactors, that aren't passively safe, are by far the safest electricity generation method we currently have. Compared to it, for example wind power is fatal (it kills people servicing the wind turbine at great heights) and solar power is fatal (it kills people on the roof, servicing the solar array, resulting in people getting fallen from the roof). Any combustion-based electricity production method should be banned right away if we need the very good safety of current nuclear reactors.
Passively safe reactors, by the way, are safe even in the hands of incompetent people. For example, the General Atomics TRIGA nuclear reactor in Finland was operated by university students. It was in the middle of a university building. No accidents happened, because it was designed to be safe. The university was very near the city center, and there were huge amounts of people living in 5 mile radius. No problem there. We could build all nuclear reactors that way: so that they can be operated in the middle of a city. That way, their waste heat could be economically utilized in city district heating.
However, current nuclear reactors aren't the only way. In current reactors, every plant is a custom design and has to be proven safe enough separately. They also aren't passively safe. However, there is nothing preventing construction of nuclear reactors in factory assembly lines, so that only the general design needs to be proven safe once, and everyone would use essentially the same reactor. They can also be made passively safe, to prevent the accident of Fukushima for example (if we consider it important enough to prevent a future Fukushima -- the death toll of the Fukushima nuclear accident by the way is far below the death toll of the tsunami that caused it; completely different orders of magnitude here).
The big mistake in nuclear power was stopping research, development and construction of new nuclear reactors in 1980s. Because of this, we don't have passively safe reactors. We don't have reactors produced in factory assembly lines (very cheap!). We don't have breeder reactors that produce enough electricity for 5 billion years. We don't have reactors that produce waste that decays to natural radioactivity in 300-400 years. We don't have thorium reactors.
The best choice, right now, if we want to have any chance of stopping the climate crisis is to construct massive amounts of all clean electricity production methods, as much as we can. This includes hydropower. This includes hydrogen-based energy storage. This includes battery-based energy storage. This includes wind power. This includes solar power. This includes current nuclear reactors. And before someone claims that we haven't solved the waste problem of current nuclear reactors, we have: Finland has geological permanent storage for nuclear waste, good for the amount of time it stays radioactive.
However, we should not stop there: we should begin the R&D to create reactors produced in assembly lines, passively safe, capable of utilizing all natural uranium and thorium in breeder mode, capable of producing waste that needs storage for only 300-400 years.
About the EU labeling, by the way, it's bullshit. They are planning to consider natural gas "sustainable". The only way it can be sustainable if it's used only for peaking power plants (so its capacity factor is below 15%) and if the carbon dioxide produced is captured and stored back underground from where the natural gas came. The massive production of baseload electricity using natural gas is nothing but foolish.