I think people discussed whether Covid will lead to a time where no one was living inside a Big Brother house because some versions ended early or were pushed back.
But there were quite a few European versions that continued despite Covid, so there was no need for Australia to keep the show on air. It was only the German one that made international headlines because they first refused to inform housemates, then were forced to inform them and made a live broadcast out of it, which went viral. But when that special aired, the versions in Israel, Italy and Sweden were also on air in Europe. Plus Brazil, Canada and the Indian ones. The Canadian and Indian versions were cancelled in March/April.
Brazil and Israel ended as scheduled in early April. Italy ended somewhat as scheduled in early April (they wanted to extend the season but reverted that decision). Both the German and Swedish version finished on the same day mid-May as scheduled. By the time these seasons finished, the Portuguese housemates have already moved into the actual Big Brother house (after living in separate apartments for two weeks and were able to Skype or Zoom with each other during that period - and that was also broadcast). And for a couple of weeks, I think they were the only ones on air. Nigeria joined them in July.
Portugal finished in early August and it was Nigeria that carried the torch for a few days before the German celebrity series and the American All-Stars season launched. The German celebrity series could have been cancelled though without breaking the streak. Nigeria ran from July to September and by then, we had a couple of seasons back on air.
so tl;dr: It was initially Germany and Sweden that kept the streak going in April and May, then it was Portugal that has done the heavy lifting till July and then Nigeria kept the streak going for a couple of days. But overall, I think Portugal deserves the most credit... and they were only able to keep the streak going because the launch was pushed back by a month. If it wasn't pushed back, there might have been two weeks in July or so with nobody living in the Big Brother house. But thanks to Australia, there would have still been Big Brother on the air continuously despite nobody living in a Big Brother house.