Steps to reproduce:
Install Bitwarden extension from Firefox store.
Click Bitwarden extension button in toolbar.
Start typing in any input box.
Press Left or Right arrow keys
Cursor should move left or right.
Orion, OS version; hardware type:
Orion: Version 0.99.117-beta (WebKit 614.1.20)
OS: MacOS Monterey v12.5 (M1)
This can be demonstrated without a Bitwarden account. The initial login / enter your password screen exhibits this behavior.
Once logged in, you can pop the extension contents out to a new window from the dropdown. Cursor keys work as expected there.