Answering my own issue. After upgrading Ubuntu, I ran into this issue:

You are missing the following 32-bit libraries, and Steam may not run:
libc.so.6

Distribution: Ubuntu
GPU: Nvidia and Intel
Despite having support for i386 sudo dpkg --add-architecture i386 and installing libc6:i386, the issue still remained even with snap, flatpak, direct .deb file or apt install. Running the steam executable directly in ~/.local/share/Steam/ubuntu12_32/steam would result in a file not found error while the file actually exists. Similar thing happens when I tried running wine, which is a 32bit program.
Apparently the issue was in a missing 32bit interpreter that probably happened with a qemu* package removal on upgrade.
To find the interpreter, I ran: sudo update-binfmts --display | grep -i i386 which showed /usr/local/bin/qemu-i386. Then, disable it: sudo update-binfmts --disable /usr/local/bin/qemu-i386; sudo systemctl restart systemd-binfmt. Now steam should run normally.

Another issue I had was that the GPU was not utilized in game, resulting in a very poor performance. This was caused by block-listing Vulkan driver and fixed by:

sudo cp -a /usr/share/vulkan/icd.d/nvidia_icd.disabled_by_nv_vulkan_wrapper /usr/share/vulkan/icd.d/nvidia_icd.json