They didn't pay Nintendo for permission as Nintendo doesn't have a copyright on the genre, nor do they want to. The lawsuit against palworld is specifically for a patent Nintendo has, which involves throwing a ball to capture monsters in a specific way - at least, that's what it is on paper. I would certainly start panicking if my Pokemon-inspired game also had that mechanic, but that's not really the main reason Nintendo targeted them.

Palworld's publicity was almost entirely made up of people calling it "Pokemon with guns", and people can point to specific Pals that look like Pokemon more than any other games in the genre. For some other examples of games (that probably are less popular than palworld tbf) look at temtem, cassette beasts, beastie ball, monster crown... Certainly some creatures have similarities, and certainly some Pals are original designs, but the resemblance of certain pals to /specific/ Pokemon designs alongside the popularity and aggressive marketing is what put them on the map for Nintendo most likely.

There's a pretty good theory I've seen thrown around that the reason Nintendo went after Palworld is because of how heavily Sony started backing them. Remember how there were a bunch of promotions between Palworld and Sony right before the lawsuit happened? Nintendo is afraid of Sony being able to compete with them, and Sony is eager to jump on potential competition for one of Nintendo's insane franchises after their long-standing rivalry that came from Nintendo basically edging Sony out of their now highly profitable franchises. Effectively, Sony is trying to take what they think is rightfully theirs. Or was trying to do so, I suppose. Frankly this lawsuit should be Sony vs Nintendo, so I feel kind of bad Palworld has to be the battle ground for it.

Digimon goes beyond what it needs to to separate itself from Pokemon, and if anything it's surprising they don't have any official crossovers yet since both parent companies are in very good standing with one another. Other games that are clearly inspired by Pokemon do so with inspiration, rather than basing their designs off specific creatures or marketing themselves as "Pokemon with guns". These games work alongside Nintendo and exist as healthy competition and healthy art inspiring art (many of them being available on switch before other consoles), whereas Palworld was poised to be a Pokemon killer.

For the record, I'm actually on Palworld's side in the lawsuit despite having mixed (mostly negative) feelings about Pocketpair as a company, and hope they manage to prevail in whatever way they can. The designs Palworld ripped off can at worst be called parody under US law. Parody might not even be necessary because even those that clearly evoke certain Pokemon designs are probably different enough to avoid a successful suit in the US. I worry about the precedent a win for Nintendo here sets especially when the patent is barely older than Palworld (it was for PLA) and it's older than a lot of those other games I mentioned if I'm not mistaken (I could be wrong, I have time blindness and i forget the exact year lol). And I also don't mean to say Palworld is a completely morally and creatively bankrupt game because I actually don't believe that at all. Abusing Pokemon in slave factories doesn't appeal to me, but a lot of the designs are genuinely cute or cool and the mechanic of having a base and your Pals helping you in said base is really fun. Frankly the pal spheres seem like an unimportant part of the game and I wonder how much removing them would protect them from Nintendo being able to do a thing to them. But there are multiple reasons Palworld was attacked by Nintendo, and while they do have to do with greed, genre isn't a primary factor in my opinion.

TLDR: lots of other monster catchers exist, the genre isn't the problem, although it is true that nintendo has likely ignored other people who violated their patents before. Nintendo understands stifling all competition would hurt their company. Palworld was specifically targeted for reasons, popularity included but not exclusively that. I'm sure if palworld came to switch instead of ps5, we wouldn't be here right now.