When upgrading from Ubuntu 21 to 22 this spring, I encountered two separate issues:
To fix the first issue, I had to enable Pipewire. It had been installed, but not turned on.
systemctl --user --now enable pipewire pipewire-pulse
It seems that Pipewire has now replaced ALSA, which was the previous sound system.
Interestingly enough, it seems Pipewire is now also responsible for Bluetooth! To fix my wireless headphones not connecting, I had to install Pipewire's bluetooth module. From Reddit:
sudo apt install libspa-0.2-bluetooth systemctl --user restart pipewire.service pipewire-pulse.service
And now I can listen to my music again.