Tundras aren’t going to be all that liveable just because the temperature is a bit nicer. They’ll still get very dark in the winter. Like 24-hour darkness, in some of it. Some people thrive, some people cope, some people go batshit crazy when daylight hours drop below about 4 hours a day.
That’s actually the easy part. Most tundra is sitting on top of permafrost. I worked on low latitude tundra for one summer and if my experience there is representative, melting permafrost is going to turn a lot of tundra into swampland for a long time.
Even if I’m wrong about the tundra turning into swampland, there isn’t really all that much room. Good luck cramming a few billion people above 55 or 60 degrees latitude.
I’m glad I’m old enough to not have to consider living at the population density you suggest. I find the population density of Saskatchewan to be quite enough. I lived in a small city (Saskatoon) for 40 years and the last 10 were flat out miserable. The first 30 were tolerable only because we escaped to nature every weekend.