Title. I’m not an achievement hunter or completionist. What’s in it for me after the story ends?

Yes, if you've played a certain previous Tales game before.

A postgame dungeon in one postgame side quest involving three cameo bosses interspersed by stronger versions of a few earlier monster bosses, and another postgame sidequest that acts as a Lord boss rush (this is the hardest content in the game). There's also the optional level 60-70 superbosses that you get sidequests for after the wedge falls and the level 99 training grounds battle if you haven't done them yet.

Beyond that, there's that SAO collaboration DLC that's coming out. And maybe some additional training grounds bosses? How the latter is going to be handled is not yet clear, since it's only apparently available on console for the time being.

The post-game side quests unlock after you beat the game, but the way it saves loads you back into the world as if you never beat it. You then decide to fast travel elsewhere and see what other stuff is available to do in the world. If you've progressed "normally" and gotten to the end, then you haven't done a lot. You have skills you haven't unlocked, dungeons you haven't played through, and bosses to fight that are all completely different. If you've come to enjoy the interactions between the characters, then there's plenty more of that too. I don't know if I'll NG+ any time very soon, but I am striving to almost 100% it on the first pass.

Added later: If you really don't care about anything you don't need to do to complete the main story of the game. Then no. But if you like the game's content (story and battle system) and generally want to experience a lot of the core of what it offers, then you should play on. There are considerably more fights and dungeons that don't take ridiculous investment time to start doing. Maybe skip powering up all of the Devil's Arms weapons because that is a time sink, but the areas to acquire them are quite nice, unique, and completely new. Post completing the game, I noticed mining ore scaled up a lot making it easier for me to create great accessories for each character making them a lot stronger too. I went through and did all of the side quests as well which had some moments, and some not-so interesting moments so there is a mixed bag.

You get the best weapons in the game hands down in the post game sub quests.