Well, actually I would like to have a toolbox to access basically everything.
Then it sounds like a toolbox/containers is a bad fit: it is additional work just to shift the “state problem” elsewhere. What I mean is you basically went from “Fedora Workstation” (or similar “traditional” distro) to “Fedora Workstation within a container in Fedora Silverblue”. If you get nothing out of containerisation, why would you spend time to maintain 2 systems instead of 1…
AFAIK, Toolbox is recommended for “everything stateful that can’t be done with flatpaks” out of simplicity and because when conflicts arise when updating (as they would also arise in Workstation), rpm-ostree (that handles the update) does not fail graciously (yet)… At least that’s what I read, not something I have personally experienced. But in principle you can always rollback, fix things and do the update again (which is exactly what happened in the reads I mentioned).
In contrast, you might feel better with the idea such conflicts would only affect toolboxes but the fix is the same anyway: if you can fix your toolboxes, you can fix an update in Silverblue.
Toolbox is a bit of a weird beast as it is though. I find it absolutely wonderful to make throw-away systems. But for actual reproducible development/deployment I would go with podman/buildah. For isolation, depending on what I want, I would go with bubblewrap or podman (or a VM in some rare cases). That being said, I know lots of people are using toolbox to maintain a long-term system-in-a-system which is fair but, to me, feels like trying to cram a square peg in a round hole with all the extra effort it involves.