> How does the planet run out of water?

By draining aquifers, for one:

* https://www.nature.com/articles/s41586-023-06879-8

* https://unu.edu/inweh/news/world-enters-era-of-global-water-...

Certain desalination exists, but can get expensive and energy-intensive (and they it may be necessary to transport the fresh water great distances).