He probably does. Or at least I assume a furnished apartment is always available. Buying "property" (and I assume in Zuckerberg terms, that means a large home or a piece of land) implies a more substantial investment and possibly a commitment to spend a much larger percentage of his time in DC.
In DC you rent an apartment to spend time at the halls of power. You need someplace to sleep and keep your stuff. Not just lobbyists, but also senators and representatives do this.
You buy a home to entertain powerful guests.
The Conways famously purchased an 8 million dollar mansion during the Trump administration, IIRC. This stuff goes on all the time. If you pay attention to these stories, you can start to understand how power really works in the US.
