I guess you ignored the big sign on the can, CAUTION: CONTAINS WORMS. Or on this board, CAUTION: CONTAINS BUTTERFLIES.
A war involving
Polyphemus is almost certainly against France or Russia, most likely France but maybe both. Just conceivably Italy or Germany; the US is out of the question. Let's say France. Never mind little secondary effects like the Anglo-German alliance. Concentrate on the direct naval aspect. All of naval development from the outbreak of war - meaning all of modern naval warfare as we know it - is instantly and totally butterflied. Gone. Almost no matter what happens in the war, so long as there is considerable combat action and resulting 'war lessons.'
In your scenario I'd really need to know more than just the
Polyphemus' war record to know what comes out of this. Presumably it looks overall bad for battleships, French torpedo boats whacking a few, and the
Polyphemus distinguishing herself by her successful action. In this case the torpedo ram becomes the ship of the future. The 'ram' part will quickly fade as torpedo performance improves.
The British need some type of ship that can keep the sea and stand up to battle; pure
Jeune Ecole is simply not an option for them. If torpedoes are the primary weapon, you do not need a huge ship to deploy them, but you need one big enough for seaworthiness and cruising range. I think the result after a couple of design generations, by the 1890s, is ships more like torpedo cruisers than
Polyphemus. The sub-like hull is not suited to seakeeping, so the hull form will be conventional. Since heavy-gun battleships are obsolete, not much armor is needed, but you'll need some, and QF guns.
But this depends also on what the French do postwar. If they are building nothing but torpedo boat flotillas for home waters, and commerce raiders, the RN has little use for ships with torpedo armament - you don't fire torpedoes at torpedo boats.
Really what you have now is an assymetrical expectation for the Next War. The British will still want to blockade French ports, to bottle up both French commerce and commerce raiders. The threat to the blockading squadrons is not French battleships, no longer built, but torpedo boats. What the RN needs in the next war are fast cruiser types, capable of defeating French raiders in a gunfight, and with plenty of QF guns to smoke French torpedo boat attacks. The British would surely also build TBDs, but they cannot base their blockading squadrons around them, because destroyer types of that era cannot keep the sea. So the blockade ships have to be bigger, not necessarily able to attack torpedo boats but able to defend against them and keep the French ports bottled up.
If the result of the 1880s war instead affirms the battleship as capital ship, subsequent development is probably still totally butterflied. In a nutshell, the classical predreadnought of the 1890s was conceived and designed entirely on theory, with nothing to go on but Lissa in 1866 - fought with first generation armored steam frigates - really not much better than Trafalgar as a guide to what would happen with 1890s tech. When naval planners were studying the
Huascar, you know they were hard up for experience of modern naval combat.

So if you throw in a major naval war in the 1890s, the lessons learned are very unlikely to lead to the classical predreadnought. More likely you get earlier all-big-gun dreadnought types, or light-armored cruiser types with nothing but 6" QF guns.