I am on another project, I will start my work later. ) Pretty much. It means that he is assigned to [work on] another project.
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harry1999I am on another project, I will start my work later. (Does ON mean working?)Yes. on = working on, assigned to, occupied with, applying time and effort on
harry1999You might be on to something... (Does ON mean something searching?)No. Not exactly. on to = on the path