Bitwarden browser extensions can be configured to exclude (i.e. explicitly not offer to save passwords for) specific domains. When a domain is in the Excluded Domains list, Bitwarden won't issue the popup offering to remember an entered password:
When a domain is in the Excluded Domains list, Bitwarden browser extensions also won't issue passkey prompts.
To configure excluded domains, open the Settings tab and select the Excluded Domains option:
Domain exclusion does not register "full" URLs, only the domain component. In the above example,
https://github.com/bitwarden/browser would resolve to
github.com when saved, meaning that the browser extension would explicitly not offer to save credentials for Github.