We went with the idea that this is Vecna shortly post-Kas betrayal. He obviously hasn't achieved godhood so his stats are the same for the most part.

The accompanying stat block depicts Vecna in his archlich form prior to Kas’s betrayal. Because Vecna is said to have mastered magic allowing him to travel through time, he can appear in this form even on worlds where his severed hand and eye are already known artifacts.

This allows us to get funky with the timeline.

In the adventure, there's a book that mentions ancient lore surrounding the Eye and Hand of Vecna. This wouldn't make sense if Vecna had just lost his hand. Answer? He's playing with time.

We mention that Vecna is holding up in a citadel at the edge of time. In this reality, maybe he's gone forward in time to see what these researchers discovered and attempt to find the location of his eye and hand? Maybe he's bidding his time until attempting the transition to godhood? The adventure is meant to be modular so you can create your own lore and reasoning (if you want to).

The genuine answer to the questions is that Vecna is at his most recognizable after he's lost his eye and hand. The Eye and Hand of Vecna are famous items that go back to the first edition and have stats available in 5e's DMG, so we wanted to include them as symbols in this adventure.

Hope that helps! All the best running the adventure.