Currently, there is no way to hide the “Organizations” pane on the right side of web vault.
Because I have a Bitwarden account only for personal use, I don’t belong to any organization and I don’t intend to.
If you have UBlock Origin, you probably can use the picker tool(don’t know if this is what the tool is called) to remove that particular element.
Kind of a temporary solution.
Remember organizations can also be personal (family or the free 2-person org for cloud hosted users).