Search is also something I was thinking about the other day. It's fine that Lemmy replaces, in part, some of the core functions of Reddit. But each Lemmy instance has it's own url. People won't be able to add site:lemmy.ml or site:beehaw.org to their search since they don't know the full list of instances and which one would have the content that they're searching for.
Time will tell how this issue will be resolved if at all.