After updating and rebooting snaps still work fine for me, but I am running the stock kernel:
amurray@sec-hirsute-amd64:~$ snap version
snap 2.48.3+21.04
snapd 2.48.3+21.04
series 16
ubuntu 21.04
kernel 5.8.0-36-generic
amurray@sec-hirsute-amd64:~$ uname -a
Linux sec-hirsute-amd64 5.8.0-36-generic #40+21.04.1-Ubuntu SMP Thu Jan 7 11:35:09 UTC 2021 x86_64 x86_64 x86_64 GNU/Linux
That message comes from snap-confine - it is launched to setup confinement for the snap and it expects to be run as root (so it can load apparmor profiles, setup seccomp filters etc) - but it would seem it is not root in your case - it is normally SUID root itself:
amurray@sec-hirsute-amd64:~$ ll /usr/lib/snapd/snap-confine
-rwsr-xr-x 1 root root 133960 Feb 8 10:53 /usr/lib/snapd/snap-confine*
amurray@sec-hirsute-amd64:~$ ll /snap/snapd/current/usr/lib/snapd/snap-confine
-rwsr-xr-x 1 root root 110792 Feb 3 06:52 /snap/snapd/current/usr/lib/snapd/snap-confine*