After discussion with @KospY, who is the author of the original idea, we agreed that I should take ownership over the mod to continue maintaining and developing it. Today, KAS is completely different from what KospY have made in 2015, but his idea is still here - we connect vessels in space! The forum thread for the initial version of KAS can be found here.
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Kerbal Attachment System (KAS)
This mod is another extensio
Thanks. Finally, I've figured it out! The issue was fixed on my side, but the updated files were never released, even though I thought they were.
I'll make and release the update one day (the legacy KAS maintenance is very low priority task). But you can fix it yourself. Open the magnet, harpoon and grapple configs and find the following string:
allowPartAttach = Disabled
And replace it to:
allowPartAttach = AllowedWithKisTool
This will fix the issue.