@nettis If you unlock your browser extension before creating any new accounts, then you will not have this problem. For security reasons, the websites where you have accounts are stored in an encrypted form in Bitwarden, which means that the browser extension has no knowledge of your existing accounts until after your vault has been unlocked.
Alternatively, after you have added a new account, you can add that website to the exclusion list under Settings > Notifications > Excluded Domains, which will prevent Bitwarden from asking about saving passwords for that domain again (it will also prevent Bitwarden from using passkeys on that domain). This alternative approach should work whether or not your browser extension is unlocked.
Finally, my personal recommendation is to completely disable the prompts (go to Settings > Notifications and disable both “Ask to add login” and “Ask to update existing login”), and instead create new accounts using the technique described in the post linked below: