So, you are proposing that the home button immediately return to the “vault” tab.
Do you also propose it clear any search results and focus the cursor in the search field so that it looks just like it did immediately after logging in? Or just return to the vault page leaving search results intact, maybe with the search filed “selected” for easy overtyping?
What do you propose should happen if clicked on an Edit page where there are unsaved changes? Discard them or first prompt for save?
Another icon possibility would be to add a Bitwarden shield icon in one of the corners and use it as a “home” button.