I don't know everything about the census and redistricting but Congress could definitely pass an extension or even a new one. Nothing in the constitution says how long it has to take. Maybe as part of the new voting rights act.
Yeah, pretty sure that the constitution requires a census to be completed every 10 years. You aren't completing a census if you don't complete it within that time frame. Not a chance in hell that holds up with SCOTUS. So they couldn't "pass an extension" most likely.
That said. Nothing in the constitution mandates that you can't do one more often. So, as you said, they could just have another one.