Seems like I was only slightly incorrect. Had two more worlds that had an issue with becoming a hive world, this time it was the stage 2 modifier that wasn't applied. Also, both worlds had been colonized normally and not taken via invasion, so it seems that the issue is with the hive world transformation in general and not related to the decision/invasion. I haven't been able to find a pattern yet, so unfortunately I don't know how to reproduce this. Here's a more detailed description:

First time: I invaded a world and decided to keep it, used the decision to transform it into a hive world. Stage 1 and 2 were applied correctly, but once stage 2 was finished and the modifier disappeared, nothing happened.

Second time: I colonized a world, intending to use it as a generator world. When stage 1 was finished, the modifier was removed and even after waiting about a month or two, nothing changed. I added the stage 2 modifier via console, even gave it the correct duration of 20 years. But once it ran out, once again nothing happened, so I had to use the console to change the planet type to hive world.

Third time: I colonized a world and made sure to not build anything apart from the bare minimums (spawning pool, etc) because I had a suspicion that that might have somehow upset the hive world transformation. I just waited and then checked again after some time, only to see that the stage 1 modifier was gone but there was no stage 2 modifier. I have now started the transformation process all over again via the decision, in hopes that that might fix it somehow.

Update: It might be related to inconsistent timer issue. I colonized 3 worlds at roughly the same time. On one of them, when I checked, the modifier was close to being timed out, and, as I waited, it disappeared with no replacement. The second world also had lost it's stage 1 modifier without it being replaced by a stage 2 modifier. On the third world, however, the modifier remained, with still 1.2 years to go.

Edit: Timer on stage 1 for the third world ran out, disappeared without being replaced by stage 2. It's been several years now on all of those worlds, and there has not been any stage 2 modifiers added, so I think it's safe to assume that simply waiting is not gonna solve this issue.

Addendum: This time, I am playing multiplayer. I am not sure if this has an adverse effect, or if I am simply being unlucky, but so far, none of my 4 colonies have managed to progress to stage 2, once the stage 1 modifier timed out.

One suspicion I was able to disprove was that it had something to do with me messing with modifiers. On one of the worlds, I had already taken the "mastery of nature" decision, which added a modifier. Another one of the worlds ended up with the naturally occuring "incomplete terraforming project" modifier. On the two more worlds, however, I specifically and intentionally refrained from doing anything at all that could alter or add modifiers in any way (like taking the mastery of nature decision) so they did not have any modifiers (apart from the always-present "biological buildings" modifier, but since that one is from this same mod, I doubt that it would be a problem). Still, despite this, as mentioned initially, none of those worlds managed to get past stage 1 transformation, and the modifier simply disappeared (and has still not been replaced by stage 2, more than a few decades later).

Something I'll have to try in a new game is to see wether it could be related to districts. Maybe if I don't build any district at all - not even a single mining or agriculture district - before the world is fully tansformed, it could have better chances of success.

Another thing that might be an issue could be blockers. This time, I did not clear any blockers on any of the worlds before the timer ran out, thinking that that might increase my chances. Next time, I'll attempt the opposite and see if I'll be more successful if I make sure to clear all blockers before the stage 1 modifier times out. Seems unlikely to be related but can't hurt to test.

The reason why I will wait with further testing until I'm forced to start a new game is that now there has already been and attempted and failed transformation, and I am not sure wether this might mess anything up even further - maybe even making transformation entirely impossible without the use of console commands. If one of the current worlds miraculously will be successfully transformed from the decision, I will of course post all the details about that here as well in hopes of further aiding with finding the issue, but I am not very hopeful that that will be the case.

Managed to transform my mining world by doing the decision and then just completely ignoring it, not doing anything at all even if I can afford it. Might be on to something. Before I took the decision, I had already built quite a few districts and buildings on that mining world, so that seems to not interfere with the transformation. Will do further tests with some more planets.

Seems like that wasn't it. Took the decision on two more worlds, then, due to the extremely long wait from lategame lag, I went to bed before it could be completed. Got up today, continued playing, timer on stage 2 ran out, world wasn't transformed. So maybe it's related to savegames, like, something isn't being saved correctly so after loading a game with the modifier already in place, the game suddenly doesn't know what to do with it? Gonna do some further testing.

Saving isn't the problem either. Took the decision on one more world, kept the game running without exiting or loading an earlier save, stage 1 still disappeared. Currently at a loss as to what might be causing it, but gonna see if I can come up with more things to try.

Ok, so whatever happened since last time I played the issue seems now fixed. Haven't done any in-depth analysis sort of thing yet but so far I didn't encounter any issues. I did colonize a Gaia World which didn't get the transformation modifier, but that might be intentional. Other than that, seems to be working. My guess is that maybe I still had some mod-stuff from other mods which didn't get properly deactivated/deleted when I disabled my other mods during the previous tests and then it somehow fixed itself maybe during one of the regular game updates.