Hydrogen has other uses too. Currently we use gas which results in carbon emissions. But with cheap enough energy, you can get hydrogen from water. There is also an option to not emit the carbon when using gas, but you get less hydrogen for the same input so no one is going to do that at scale.

Another major use for hydrogen is the haber-bosch process.

That's why it will never IMO be feasible until we have surplus electric power that it can be made with. Power that would otherwise be wasted.

Yes, but it can be stored where batteries lose power over time. And a lot of the infrastructure doesn't need to be build but can be converted from natural gas use.

In the end batteries and hydrogen fill two very different gaps. You can use batteries to shift the renewable production peak at noon (thanks solar) to the demand peak in the evening, maybe even flatten fluctuation (in production and demand) over a few days. But they are entirely useless as seasonal long-term storage.

Also plans to produce green hydrogen exist independently. It's a requirement to decarbonise a lot of industry processes where direct use of electricity doesn't work. It's also a raw material in chemical industry.

So if decarbonisation of more than just electricity production is the goal, large scale hydrogen production is a given. As is large scale storage as production from renewable energy will always have seasonal fluctuations. From there having it also double as long-term on-demand stored energy means just scaling up what is already there.

The world is currently at 42.6% green electricity. Also 100years are a very long time.

True, but with a constant 100% plus generation from renewable, there obviously wouldn't be any fossil fuel burned to generate electricity. Here we are already at 80% of our total yearly electricity generated by renewables.
When that reaches 100%, it can be done by utilizing surplus at peaks to generate hydrogen, exactly to completely prevent any use of fossil fuels.

I don’t see the whole worlds energy consumption going purely green within the next 100 years.

100 years is a very long time, back in the 70's it was considered a lofty goal to achieve even 10%, and now we are at 80!!
I don't think you have historical perspective.
Personally I think within another decade we will surpass 100% here, and have the ability to export a lot of surplus renewable energy.
I was also mostly thinking about civilized countries, not so much for instance USA.

Local today global tomorrow.

One of the reasons. The other ones are Russia and China wanting to split the West and low birth rates meaning the low cost workers are harder to come by(2/3of the growth in the 25-64 year old population will be in Africa in the next 25years and the richer the country the more likely a shrinking workforce, so imagine unions lowering the work week or similar).