Trying to install a package from bullseye-backports

I am running Debian Bullseye and I want to install ffmpeg 4.4.1, which looks to be available in sid : So I have added the backports repo :

# apt-cache policy
Package files:
...
 500 http://mirrors.ocf.berkeley.edu/debian  bullseye/main amd64 Packages
     release v=11.2,o=Debian,a=stable,n=bullseye,l=Debian,c=main,b=amd64
     origin mirrors.ocf.berkeley.edu
 100 http://deb.debian.org/debian  bullseye-backports/main amd64 Packages
     release o=Debian Backports,a=bullseye-backports,n=bullseye-backports,l=Debian Backports,c=main,b=amd64
     origin deb.debian.org
...

# apt-get install -t bullseye-backports ffmpeg
Reading package lists... Done
Building dependency tree... Done
Reading state information... Done
ffmpeg is already the newest version (7:4.3.3-0+deb11u1).
0 upgraded, 0 newly installed, 0 to remove and 33 not upgraded.

apt-cache show ffmpeg only shows one entry, which is for ffmpeg 4.3 in the main stable repository. Any advice?