I’ve moved your post to the feature suggestion section.
For clarification… the icon you see is the reference to a library (not technically a server reference).
There’s an existing suggestion discussing an option to have custom icons for libraries – though that’s targeting a wider context (not just how those libraries are represented on watchlist items).
However… if that’s what you’re aiming for, it might make more sense to comment/vote in that existing thread in order avoid distracting votes.