In general, in container-based workflows, you usually don’t update the components within containers from within the container. Though technically there is nothing stopping you from running dnf upgrade from within the container.
Typically, for containers, you want to update the underlying container image. In the case of toolbox, the podman container is “fedora-toolbox”. And you can update it by running podman image pull <image name>:<tag>. If there is a newer version of the container, this will pull it and update it as necessary.
For Example:
yosuke@Yosuke-Thinkpad$ podman image list
REPOSITORY TAG IMAGE ID CREATED SIZE
registry.fedoraproject.org/fedora-toolbox 36 1113918107fb 2 weeks ago 496 MB
yosuke@Yosuke-Thinkpad$ podman image pull fedora-toolbox:36
Trying to pull registry.fedoraproject.org/fedora-toolbox:36...
Getting image source signatures
Copying blob e6ba7c6e6f56 skipped: already exists
Copying blob 2bfab29d2ca9 skipped: already exists
Copying config 1113918107 done
Writing manifest to image destination
Storing signatures
1113918107fb793917c01c4ecbeb94ff66a48bd2c9aa5a12b3dfd0332143fd9b