apt-get install python3.10 doesn't?

My WSL2-based Ubuntu is running python 3.8.10. I'd like to update it to 3.10.x, so I typed:

sudo apt-get install python3.10

That produced a lot of output and appeared to complete without error, but at the end, I still got:

$ python3 --versionPython 3.8.10

...even after quitting the WSL2 shell and starting another. Did I miss a step?