https://www.usaid.gov/news-information/press-releases/oct-04-2024-united-states-announces-humanitarian-assistance-support-populations-impacted-conflict-lebanon

Lebanon isn't a cohesive country with a single government. Southern Lebanon is controlled by Hezbollah, and (mostly) populated by Shiite Muslims. Northern Lebanon is mostly populated by Christians (about 40% of the total population), with a mostly separate government. The Christians have been trying to prevent Hezbollah and their supporters from fleeing north.

The US isn't necessarily "funding both sides" by sending a small amount of humanitarian aid to one group, and a much larger amount (10x) of weapons to another (though even then, most of the funding is going to anti-air defense).

If you want to make that argument, you need to drill down to exactly where that money to Lebanon is actually going. This isn't Gaza; with Gaza it's much easier to make the claim that the US was funding both sides as Gaza has (had?) a cohesive singular government: Hamas.