This is probably a better link to how do advanced searches (using Lunr), since it actually tells how to do them in Bitwarden:
https://help.bitwarden.com/article/searching-vault/#advanced-search-examples
In particular, putting this in the search field is supposed to show only your personal items (items without a collection):
>-organizationid:*
Having said that, these searches don’t work on the Bitwarden web site, and although they seemed to work in the Safari browser plugin, it ended up breaking the UI.
I would also really like to have some sort of ability to quickly switch between looking at my personal items and organization items.