Yes, I enjoy working with this client and I see it as an opportunity to showcase my talent on other platforms. I just wasn't sure if I need to mention Upwork in any way. Do I need to link my Upwork profile as well?
re: "I just wanted to make sure that Upwork doesn't have any particular stipulation."
Upwork has no rules about this at all. Upwork has no interest in controlling who you lend your name to or what you do with your biography.
You do NOT need to mention Upwork in any bios.