Naval intelligence was a core institution before 1914

How seriously did navies before the First World War prioritize intelligence about rival ships?

Very seriously; the Royal Navy sustained intelligence work for centuries, and its dedicated division became one of the Admiralty's largest institutions.

The Royal Navy maintained intelligence work through the Age of Sail because it needed information about rival ships and fleets. Its Naval Intelligence Division is recalled as a particularly large part of the Admiralty, with operational functions later separated into their own branches. The recollection gives it roughly sixty years as the largest division, although no dates establish that institutional sequence here. Intelligence remained a major activity after the reorganization. Other navies also pursued information about opponents and considered where they could obtain it, making collection a continuing peacetime concern.