Is Save the World fun/worth buying? I feel sure as soon as I will buy it, it'll go free to play.
It has some fun-though-inconsequential/fairly superficial writing that's 100% just spoken dialogue/monologue during & in between missions that you just listen in the menus or during the initial minutes of missions (and maybe when achieving some mid mission goals). There are no cutscenes. Not the most engaging style of storytelling, even if most of the characters are fun, but it makes for an entertaining listen. Too bad you can't listen to anything ever again so if you miss something because you got distracted, tough luck (unless someone has saved all the dialogue to Youtube or something).
As a game... there's a good game under too much super-grindy, nearly endless "look-numbers-go-up" gacha/F2P leveling up & the mission types end up being fairly repetitive in the long run. The base building tower defense aspect is fun, especially the persistent base in each region, but the game gives way too little materials so gathering materials is a bit too prominent a part of the game when doing normal missions, especially if you end up being the one to do most of the building just because you don't want to waste your time with countless failed missions because no one else knows what the fuck they are doing or what kind of defenses you need at minimum to survive missions.
If you're alone, I'm not sure if I'd recommend it. The random team mates can be such a shitshow (they don't build, they leave the game mid mission after you've already spent thousands of materials, they are shitty players who don't know how to play the game, they don't help you), especially later on when solo-ing basic missions starts not being feasible (it's possible but you'd need an insane amount of materials and gathering those will take forever). Early missions are more soloable or at least not as much of a disaster with shitty team mates, especially with some leveling, so you might find yourself thinking you can get all the way through but the last region in particular stops being fun. It just ramps up the difficulty way too much and no amount of leveling seemed to make them more tolerable.
If you can find 2-3 people to play STW with, then it might be worth all the downsides but alone it's just a huge slog of a grind because you can't rely on having 2-3 decent team mates 80% of the time.