Means ridiculously enthusiastic and ready to crack on, like you’ve been waiting by the door since yesterday. It’s a slightly old-fashioned British saying, often said with a grin when someone’s a bit too eager. The mustard bit likely nods to mustard being keen meaning sharp and punchy. Still pops up in workplaces and family chats.
"She’s keen as mustard to start the new project, turns up at 7:45 with a colour-coded spreadsheet and a Tesco meal deal, acting like she runs the place."