More info from a different article that provides context:
Bypassing Congress with emergency determinations for arms sales is an unusual step that has in the past met resistance from lawmakers, who normally have a period of time to weigh in on proposed weapons transfers and, in some cases, block them.
In May 2019, then-Secretary of State Mike Pompeo made an emergency determination for an $8.1 billion sale of weapons to Saudi Arabia, the United Arab Emirates and Jordan after it became clear that the Trump administration would have trouble overcoming lawmakers’ concerns about the Saudi and UAE-led war in Yemen.
Pompeo came under heavy criticism for the move, which some believed may have violated the law because many of the weapons involved had yet to be built and could not be delivered urgently. But he was cleared of any wrongdoing after an internal investigation.
At least four administrations have used the authority since 1979. President George H.W. Bush’s administration used it during the Gulf War to get arms quickly to Saudi Arabia.
As others pointed out, this appears to only apply to arms sales, not for aid packages as in the case of Ukraine.
It looks like there's some precedent for workarounds that FDR used to aid the UK when Isolationists didn't want to help during WWII, and that Biden has already been doing a good chunk of it. Without direct cash, I do think there are fewer options, but I'm curious what will happen if an aid package isn't passed by Congress in early 2024 once the current one runs out.
Politico: The WWII Strategy Biden Can Use to Bypass Republicans on Ukraine
...