The Vault button opens the Vault view, the Settings button opens the Settings View, the Generator button opens the Generator view, etc. If the Vault view is the “main” view for you (as it is for most users), then maybe after a little bit of time using the extension, you will remember that the main view in Bitwarden’s browser extension is named “Vault” (allowing you to find the corresponding button in the navigation menu).
This is not an uncommon UI structure.
Here is Adobe Acrobat — there is no “Back” button to return to the “Home” tab:
Here is Microsoft Excel — again, there is no “Back” button to return to the “Home” tab:
What I do agree with, is that the browser extension UI could benefit from a universally available “Home” button, as described in the following Feature Request (which you might consider supporting):