If the November election unseats the current administration, I wouldn't be surprised if we have some kind of do-over with the census. Something on the order of sending census takers back out into the field next fall (when things hopefully will be back to somewhat normal) to pick up those who are missed this year.
That would meet a constitutional challenge and one the administration wouldn’t win
Not necessarily. The census is conducted under the authority of Congress and the administration could get congressional approval. I think Congress would okay it because enough legislators on both sides would want the census to not undercount communities in their state and would likely be getting pressure from their own state government and their constituents.
Also any state, county or local government could ask for a special census if they believe that there is a significant increase in their communities due to growth or annexation. "Growth" would likely include an influx of students who studied remotely one year but on-campus the next. The government requesting the special census would have to pay for it, but the cost may be more than offset by increased revenue from the feds that could result from the special census.
They should know by March 31 whether a special census is necessary. That's the date the Census Bureau is supposed to provide data to states for redistricting purposes.