Tsushima actually had a very interesting effect, and some surprising personalities offered divergent opinions on what the lessons were.

We should first note that even before the battle there was a movement towards battleships that were larger, faster, and mounted more heavy guns. This "ideal battleship" was initially the brainchild of Italian architect Vittorio Cuniberti, and expanded upon in various editions of Jane's. A cause soon to be taken up by the irrepressible Jackie Fisher late CinC of the Mediterranean Fleet and then 2nd Sea Lord and then CinC Portsmouth before First Sea Lord. Cuniberti would also go on to have an impact on the design of Russia's first dreadnought class, the Gangut's who had a tortured history through several iterations and squabbles over their specifics and construction.

To this side the lesson was stark. Togo's fleet could use its superior speed to wait and engage the Russian's at will, and to ensure superior positioning when doing so. While the need for more large guns was clear. At a time when training and gunnery drills regularly focused on ranges of no more than about 5,000 yards, the Russian fleet in desperation opened up with straddling salvos at 19,000 yards, and scored main battery hits at 14,000. And it was a long range main battery hit on the Russian flagship Suvorov that killed most of the bridge crew and wounding the admiral causing the ship to draw out of line further confusing the fleet and diminishing its fighting ability.

While at the same time the smaller guns only made fire control more difficult and could not engage at range while the 12in main batteries were doing most of the real work.

This was not a universal opinion though. In the US the great naval strategist, Alfred Thayer Mahan in fact reached the opposite conclusion. That a larger battery of intermediate guns was preferable, along with dismissing the need for superior speed over every enemy.

Mahan noted the various reports the murderous work that the IJN secondary guns had done to the crew and lightly armored superstructures of the Russian fleet. Attesting that guns which would prevent the crew from fighting the ship were more important than just lobbing large shells in the ships direction slowly.

This ignored though the fact that by the time those guns were brought into use the battle was already all but decided, while the rise in quality and usage of the torpedo meant that ships had even fewer reasons to close the range.

However by that time even so short after Tsushima the plan for the 1st US dreadnoughts were already taking shape in the South Carolina class. At the behest of President Roosevelt, then Commander William Sims, USN Gunnery Chief, answered much of Mahan's critique and the South Carolina's went forward, arguably the most forward thinking of any 1st attempt at a battleship. Sims would later command all USN forces in Europe in WW1.

Dreadnought: A History of the Modern battleship by Richard Hough

From Dreadnought to Scapa Flow: The Royal Navy in the Fisher Era, Volume I Arthur Marder