When Bitwarned becomes the default autofill provider in the browser (chrome.privacy API), it stops the browser from handling standard non-password forms, like search inputs or similar; it does not save the input and does not suggest previously submitted data. Bear in mind that these inputs are not cards or identity fields, but just standard form inputs.
FYI, the example you have shown is an identity field.
You should be able to solve this by disabling the option “Make Bitwarden your default password manager” under Settings > Auto-fill. However, there have been reports that doing so doesn’t always work, in which case the solution is to uninstall and reinstall the browser extension, and to subsequently ensure that “Make Bitwarden your default password manager” remains disabled (e.g., click “Ignore” if prompted to make Bitwarden the default password manager). You may then additionally need to access your browser’s auto-fill settings (e.g., chrome://settings/addresses and chrome://settings/payments) to ensure that the options for the browser to save and fill non-password data are enabled.
