This happens because of something funky happening with the libwlroots-0.18 package (one of the libraries sway depends on). With the default configuration, running apt install sway will install sway from the upstream debian repository. But the raspberry pi folks build their own libwlroots-0.18 package, with a version string that makes it seem newer than the upstream debian one. So the raspberry pi package gets installed and sway throws this error.
I fixed it with a small apt configuration fragment that tells apt to lower the raspberry pi archive priority for the libwlroots-0.18 package, so that the upstream debian one is used. sway now works properly, and I’ve not noticed any other problems (yet) from using this package instead.
To do this, create a file /etc/apt/preferences.d/10-libwlroots-0.18-pin.conf containing:
Package: libwlroots-0.18
Pin: origin "archive.raspberrypi.com"
Pin-Priority: -10
After saving that, you’ll have to remove and reinstall the package. I ended up running
sudo apt purge libwlroots-0.18
sudo apt install sway
and sway now works.