Well, “blocked aid” can be a little ambiguous. Private organizations in the US are allowed to fund UNRWA and have done so, see for example https://www.unrwa.org/newsroom/news-releases/unrwa-usa-resumes-funding-un-agency-palestine-refugees-providing-5-million

What remains paused (and what the bill you reference is trying to unpause early) is, along with New Zealand, US gov’t funding to the agency, which currently is scheduled to be lifted (rather late) on March 2025 as per https://unwatch.org/updated-list-of-countries-suspending-unwra-funding/

That’s still quite bad, but it’s not as bad as preventing individual US donors too.