Funny, the two you’ve heard of are the two I hadn’t heard of. Goldendoodle vaguely rings a bell, but goldenrod was a complete mystery to me. Golden goose is a reasonably common English expression, referencing one of Aesop’s fables (or possibly an unrelated fairy tale, though I personally am not familiar with that fairy tale).

Golden parachute is an expression for a payout a high level executive gets if they get fired, especially as part of a merger or acquisition.