It seems like the supreme court staff would all be furloughed though. Could probably cut power to the buildings too. With a little creativity they could certainly create a situation where the supreme court stops getting paid and there is no way to convene the court to deal with it.
https://www.reuters.com/legal/government/us-judiciary-can-keep-operating-2-weeks-if-government-shuts-down-2023-09-19/
It seems like the supreme court staff would all be furloughed though. Could probably cut power to the buildings too. With a little creativity they could certainly create a situation where the supreme court stops getting paid and there is no way to convene the court to deal with it.