In terms of story, I'm with most people in that it wasn't particularly gripping, but for the most part I got the impression that it wasn't really trying to be. This also made it feel tonally confused at times, though. The death scene that vanguard333 mentioned was a great example of that, especially since Alear mentioned not having much attachment to her shortly before that due to their amnesia, and yet there they were, crying their eyes out with the rest of the characters. It was like the story wanted to get straight to as many gut punches as possible without working to make the payoff worthwhile. Not every story has to be as grave as 3H, so if the game was going for a lighter touch, I just wish it stayed that way instead of lurching awkwardly in a more serious direction at times.
That's fine, though, because the gameplay was among my favorite in the series. Engage was the first game where I started with Maddening, because I thought back to my experience with 3H on Hard and how the gameplay there felt like more of a formality on that difficulty. I wanted to struggle a bit this time, and I struggled plenty. The emblems are probably my favorite singular addition to the series because of how powerful they made me feel. I liked the idea that you were obliged to choose carefully when to Engage, because when the proper moment was chosen, it always felt like you were either setting the tide of battle or turning it back in your favor. Corrin was the MVP for me, because her terrain-generating powers were handy in some way in pretty much every situation paired with Alear. I also enjoyed silly shenanigans like warping my entire team in a single turn with Micaiah or sending my allegedly immobile general halfway across the map with Sigurd.
One thing I found funny about Maddening difficulty was how the "smarter" AI sometimes was abusable. What springs to mind is how if an enemy has no chance of damaging a unit, they'll avoid combat with that unit--even if that person is their only way through. It makes me remember how in Ike's paralogue I sat Louis on one chokepoint and Zelkov in constant fog in another. The enemies saw no way to damage the only units they could reach, so I was free to pick the ones even further back with longer ranged combatants. But, if this was Hard, where the enemies would have suicided and the sages would have been able to get through and ignore Zelkov's terrain bonuses, I would have been doomed. Also, Lyn's clones were a godsend. I'm glad that for whatever reason, the enemy considers those to be more valuable targets than my actual units just because they can be killed.
There were a lot of turtling situations like that, because I'm not fussed about LTCing, and it's probably why the chapters I found the most aggravating were the ones where that wasn't possible. There was the chapter with a turn limit where you had to dispatch the boss while being hit by avalanches and being swarmed by enemies, and I had to get through that by attacking the boss from the other side of the map and making him come to me. There was also the final chapter where the endless swarms of reinforcements had me resorting to just only halfway dealing with the gimmick of the map and then muscling my way through.
I suppose that's the reason I haven't felt a strong urge to replay it since it came out in January. It felt like I had "solved" each of the maps, unlike in other entries in the franchise where I felt free to explore other characters and strategies on another playthrough, and there didn't seem like much of a point of going through the same motions. As many have raised, going through the Somniel also dulls the urge, because that was a slog even the first time through, and I'm not sure if I would have made it through if I skipped everything. That said, it was the first game where I went for the "big boy" mode and stuck with it, so maybe fans with more exposure to that level of difficulty can attest to the way forward being similarly limited in other entries. At any rate, I played before any of the patches and without any DLC, so maybe with enough time, that'll present enough of a fresh experience that I'll want to return.
Finally, although I don't remember most of the music, the first battle preparation track has to be my favorite of its kind in the series. The energetic violin/synth combo really hyped me up each time to get ready to tackle another challenge--one that would require clever thinking, but was always surmountable.