The existence of Yamato shouldn't result in any changes to battleship fleet compositions in 1916, because no one is going to be in a position to lay down new battleship designs until postwar.
True for the RN and lesser powers in Europe, although it will set designers and shipyards think. The US might decide its 1916 programme isn't enough - if it does get anything like accurate details of the size of the Yamato. What they will come up with and how practical it would be could be interesting.
Japan nearly walked on the treaty in our timeline because of the US and Great Britain ganging up to insist on the 5:5:3 ratio, and this betrayal pretty much single-handedly caused them to break off their longstanding alliance with Great Britain. There is absolutely no way they're going to allow 5:5:3 in an alternate history when they have the upper hand. Indeed, the only reason they'd actually allow a parity ratio in "superheavy battleships" is that they're justifiably confident that neither the United States nor Great Britain can build a battleship on par with the literally divinely granted Yamato.
Good point on what stance Japan might take. Especially if the DT government is persuaded by the UP people that they have a clear technological lead for at least a decade or so. Although if they learn what happened to UT Japan they might be more cautious about the idea of too much tension with the US. Mind you what they might do is agree terms say on a 5:5:3 ratio but avoid any agreement on other classes, other than definitions and secretly do as much work as they can on carriers, aircraft and related technology. Have the US and possibly the UK spending massive amounts on very large and expensive ships which quickly become obsolete.
Actually Japan wanted to maintain the alliance, both because it gave some safeguards and also diplomatic prestige. It was the US that insisted on the alliance - despite it being clearly defensive and the US even then having a loop-hole for an attack on Japan not triggering a Britain response. Britain was divided on the issue as were the dominion - Australia and New Zealand wanted it to continue and Canada wanted it ended for better relations with the US and it was the US insistence that it ended as part of the terms of the WNT.
And even with Japan being willing to allow parity, the U.S. and Great Britain are going to have to make numerous secondary concessions to get there as opposed to something like a 3:2:2:1:1 battleship ratio in Japan's favor. Literally the only way Japan would even consider conceding 5:5:3 in this timeline is if they're fielding three Yamatos while the USN and RN are restricted to 16" guns and 35,000 tons.
I can't see either US or UK being willing to accept parity as they still see themselves as world wide power while their view of Japan is as a purely region one, plus it would definitely be a red flag for the fire-eaters in the US. Also while the Yamato is a big boost, probably most in terms of the knowledge it presents rather than the ship itself the DTs should fairly quickly be aware that there might be problems maintaining some aspects of the ship and also that while its a very powerful ship its a single one.