Landfills are tiny relative to usable land and are eventually just capped and turned into parks.
Most of the popular fear about running out of landfill space can be traced back to a misused statistic about small rural landfills being decommissioned. RCRA Subtitle D regs basically have driven the shutdown of old town dumps. Modern landfills are much more efficient, with better safety controls for leaching and gas capture, better compression and sorting, and even processes that speed decomposition. The headlines will scream that the number of available landfills are dropping rapidly and neglect to mention that total capacity is actually up and total disposed volume has been trending down since 2000, even despite population increases.
Highly recommend touring a landfill and learning about waste management at scale.
There are really interesting engineering dilemmas that are always a step more nuanced than "we must use x solution or fill the world with trash."