Currently the Ctrl+F shortcut is used for searching for rooms joined, not for searching a room's history and I'm not aware other shortcuts for searching history. It would be nice to have such a shortcut because the search button is currently not very discoverable (IMO). Preferably Ctrl+F, and use another shortcut for searching for rooms.
I would add this, but I'm honestly scratching my head on what we could use. CTRL+F is for the room switcher, CTRL+SHIFT+F is for searching members.... CTRL+ALT+F? Or maybe make CTRL+SHIFT+F make it search for messages, I do that way more often than looking for a specific user.
I'd argue the most important action would be searching through room history, and thus should be the one with Ctrl+F assigned. Other chat applications don't care at all about keyboard shortcuts for searching rooms or members: Nheko, Discord and Telegram only have room history search shortcuts (Telegram optionally lets you search through the history of all your rooms as well). I could see Ctrl+Shift+F for searching rooms since the user may be in more than 20 groups, though the point is weakened by the fact rooms can be organized into spaces and Neochat separates them neatly. But I don't really see a use case for searching members that is done often enough to warrant a shortcut.