... Now, my feeling tells me that "introducing myself" is more common and logical, while "introducing information about myself" is also logical in some contexts.
The problem is that the verb "to introduce" has (at least) two meanings.
One meaning is to tell someone something about a person: his or her name and perhaps more. In that usage, you only introduce a person. You cannot introduce information about a person.
A second meaning is to put one thing into another thing. One can, for example, introduce a topic into a discussion, a chemical into a solution, or a control rod into a nuclear reactor core. In that context, you could introduce information about yourself into a book. Therefore, "introduce information about myself" is (as you wrote) correct in some contexts, but those contexts are not the context of someone introducing himself at a meeting.
In the context that you provided in post #4, only "introduce yourself" is correct. "Introduce information about yourself" is an error. The manager may have made this error because he or she remembers a sentence in which the word "introduce" is used with its other meaning, and does not understand that the two meanings are different.