No. You cannot.
Amber is designed to listen for the requests your clients send to ask for event signing. No password manager I'm aware of is designed to do that.
Don't forget: every thing that happens on nostr is signed. Post a note? Signed. React? Signed. Upload media? Signed. Unsigned events are basically ignored.
Your nsec is a key, one of a pair with your npub. In order to unlock "doing something" you need both, like the silly two-key missile launch systems. Without both, you can't do anything.
You aren't logging in. You are giving permission to sign events with your keys.
That's a huge difference, and why a password manager cannot sign nostr events.