Completing a task no one asked of me (

) ... the Battle of Cape Engaño ...
Recapping a bit, the IJN battle plan was to use a carrier force coming from Japan to lure Halsey's fleet away from Leyte Gulf so that a major IJN surface fleet could enter the gulf and wreak havoc on the transports and cargo ships supporting the Leyte invasion. While the smaller surface fleet that tried to enter Leyte Gulf through Surigao Strait is traditionally viewed as a plan complicating pincer move, it seems possible that it had a dual purpose: to lure 7th Fleet surface elements away from the gulf; survivors,
if any, to attack whatever they found in the gulf. IOW, the big picture would have been: Admiral Ozawa luring away Halsey's fleet; Nishimura luring away Oldendorf's battleships and cruisers; Kurita free to wreak havoc without opposing battleships, cruisers, and fleet carriers.
Bait or pincer, Oldendorf's battleships and cruisers blocked and sank Nishimura's much smaller battleship force. Believing Kurita had reversed course and was heading for home, Halsey took Ozawa's bait. In reality, Kurita had reversed course temporarily to regroup and make the last part of his run for Leyte Gulf in darkness (whether or not he knew it, Kurita was out of range of US land-based recon, and USN night carrier operations were yet in the future).
So, what was Ozawa's bait? Ozawa's force was centered on fleet carrier Zuikaku (the last surviving carrier that had taken part in the PH attack) and light carriers Zuiho, Chitose, and Chiyoda. Also in his force were Ise and Hyuga, battleships whose rear turrets had been replaced with a hangar and flight deck.
Reversing the tape a bit, 8 days prior to the invasion at Leyte, Halsey's fleet attacked Japanese airbases at Formosa, to neutralize them so they could not cause problems for the Leyte invasion. The Japanese mistook this for an invasion and took the 3/4-trained airgroups from IJN carriers and threw them into that battle. Being under-trained, losses were heavy. As a consequence, Ozawa's carriers had almost nothing in the way of airgroups. It is very possible that the USN - and therefore Halsey - was unaware that Ozawa posed no air threat. Regardless of what was known in that respect, it was understood that it is quicker to train pilots than it is to build an aircraft carrier. So Ozawa's carriers had significant value beyond whatever planes they brought into battle.
With that lengthy prelude ... Halsey knew Ozawa was coming in a carrier force. So while most of his airgroups were attacking Kurita in the Battle of the Sibuyan Sea, he also had search planes north of his fleet looking for Ozawa, and toward the end of the day Ozawa was found. Thinking Kurita was heading for home, Halsey took Ozawa's bait and took his whole force toward Ozawa. During the night Halsey sent his battleships and cruisers a couple miles ahead of his carriers. This had several purposes: they would be a gauntlet any IJN planes or surface forces would have to run; they would have a head start toward mopping up damaged IJN ships in the aftermath of the many waves of air attacks.
The battle is pretty easily described. A pre-dawn search located Ozawa. Once it was known where to go, wave after wave of air attacks - all day long - sank Zuikaku, Zuiho, and Chitose, and crippled Chiyoda. While urgent radio messages regarding the Battle off Samar started being broadcast fairly early in the morning, word seems not to have reached Halsey for some time. Consequently it was around 11:15 that Halsey had his force turn around, but then his destroyers had to be refueled. A small cruiser group was sent toward Ozawa's devastated force, which sank Chiyoda. After the refueling, Halsey's force was too late to participate at Samar (though not knowing where Halsey was probably influenced Kurita's decision to retreat), just sinking a destroyer straggler.
Was Halsey's northward move a mistake? It is widely condemned as such, though generally in light of what Halsey did not know. The information Halsey had as things were happening showed Kurita in retreat and Ozawa's force was probably not known to be de-fanged. IMO, Halsey was aggressive, but not foolishly so, and was not aware he was pursuing a decoy. In light of the research by Anthony Tully, presented in his book
The Battle of Surigao Strait, it seem likely that Kinkaid, commander of the 7th Fleet, also sent Oldendorf after a decoy force led by Nishimura.
So, how to sum up? The USN lost a couple of escort carriers, with a couple more damaged. A light carrier was lost to a Kamikaze, and a light cruiser attempting to assist had heavy casualties when ordnance on the carrier baked off. A couple of destroyers a destroyer escort were lost while defending the escort carriers. Another destroyer was heavily damaged at Surigao Strait.
The IJN lost one of their largest and newest battleships plus two old battleships (a perfect gambit, too potent to ignore but the least potent among the IJN's battleships). The IJN lost its last fleet carrier and three light carriers. In the major engagements and mop-up the IJN lost several heavy and light cruisers and several destroyers.
In ships and men, the IJN was the big loser. On a strategic level the Imperial Japanese Navy was reduced to a few major elements, but could hardly be called a fleet or a navy. Similarly, Leyte and the Philippines were more than so many square miles of land. By controlling the Philippines the US effectively blockaded the Luzon Strait, cutting off the industrial base in the Japanese home islands from many raw materials those industries needed. This, in turn, allowed many USN submarines that had patrolled the strait to be concentrated around the Japanese home islands.