https://imgur.com/a/lPjhvl6

Got this error, with "K2SO" + "Any Planet Start" installed. Disabling "Any Planet Start" from active mods removing this error.

Unfortunately, this mod isn't compatible with K2SO.
The only reason I haven't marked it as such is case someone comes along and wants to add compatibility themselves.

I see... Is the incompatibility purely technical, or does it also stem from the impossibility of progression through the tech tree at some point?

I don't know too much about the progression of K2SO so I can't speak on the progression side of things, but from what I know it's mostly a technical one.
Looking at the error message for example, it looks like K2SO tries to modify a technology after APS has changed it, (rightfully) assuming some data is present in that tech and making an attempt to access it, resulting in said error.

That specific error would most likely go away if I make APS run after K2SO, but I imagine there would be more errors like that regardless of load order.
Either way, I personally don't have the time to invest into making compatibility work; I haven't even played K2SO so I'd have no idea where to even begin with that. If someone else was investigating it, I'd be happy to make any necessary changes in APS (e.g. the load order change) to make it happen though.

I dug into it a bit, and after a few changes I managed to get APS working with K2SO.
The first issue was load order. APS needs to load after base Krastorio2, otherwise K2 can crash when it tries to modify technologies that APS has already converted to research triggers. Adding a hidden optional dependency on Krastorio2 fixed that part.
And there is something important. APS should not have an optional dependency on Krastorio2-spaced-out. K2SO already has its own APS compatibility code, so K2SO needs to load after APS. If APS is forced to load after K2SO instead, that compatibility code runs too early and you can end up with tech-tree cycles like steam-power -> fluid-handling -> steam-power.
The other small issue was in the Fulgora scrap productivity techs. APS removed science packs by setting specific array entries to nil, which breaks if another mod adds extra packs because it can leave holes in the ingredients table. I changed that to remove the extra packs cleanly from the end of the list instead.

So in the end the actual changes were pretty minor: add a hidden optional dependency on Krastorio2, keep K2SO loading after APS, and make the Fulgora science-pack trimming a bit more robust. After that, it started working for me.

To be more specific I changed this:

scrap_3.unit.ingredients[5] = nil
scrap_2.unit.ingredients[4] = nil
scrap_1.unit.ingredients[3] = nil

to this:

while #scrap_3.unit.ingredients > 4 do
table.remove(scrap_3.unit.ingredients)
end

while #scrap_2.unit.ingredients > 3 do
table.remove(scrap_2.unit.ingredients)
end

while #scrap_1.unit.ingredients > 2 do
table.remove(scrap_1.unit.ingredients)
end

Edit: Oh I forgot to mention that I tested only with Fulgora as a starter planet, not sure how it will work with other...

That was all on the technical side of getting the mods to work together, but there are still a few softlocks in places where K2SO changes the tech tree.
Do you want me to report those to you as I find them, or would you rather I just make a separate compatibility mod when I have the time?

My stance on compatibility for APS so far has been to keep things in separate mods, partially because I don't want to be held responsible for it, and more importantly so if the compatibility needs to be updated, nobody's waiting on me to do it.

I just released an update with a hidden optional dependency on K2 and with the scrap productivity fix, let me know if there's anything else I need to do.
As a side note, if/when you're making the compatibility mod, feel free to require the utils file from APS, that exists for both myself and anyone else doing APS compatibility, makes handling technology changes a lot easier.

I messaged Polka about it. Right now everything works when starting on Fulgora or Gleba, but the Vulcanus crash is much easier to fix on the K2SO side.
I also asked whether she’d be okay with me making a separate compatibility mod, or if she’d rather keep the compatibility work inside K2SO and finish it there herself. Once I get her answer, I’ll know which direction to take and can start working on the remaining compatibility issues.
Thank you for the update!

No problem, good luck!