NotAffine

You're thinking of Publisher now, right?

Unfortunately, that's all Affinity is capable of. I was recently looking for previous requests about setting the resample algorithm per image in Publisher, but I didn’t really have the energy to submit a new request — it seems to be futile.

The one who helped me combine the shapes originally said Affinity gets said to fix that since around 2015 and they still haven't done that. Of course I can't just believe such a loose statement but if that's remotely true it's pretty sad.
This makes working with symmetrical shapes (which are quite common) soo much worse than in Illustrator. If you have a bigger project with symmetrical shapes you'll loose hours on these small details.

Exactly. I managed to do it with a different method but it was a comparable effort to do so. This could be improved greatly by "just" fixing the snapping, I think. Or, if the actual problem arises because of some problems with the shapes themselves, there should be an option to see/fix those issues!
Do you agree?

So I tried making a shuriken. For that, I wanted (at first) to make a triangle and cut out a bit of that in the middle. I made a quite simple shape, wanted to duplicate that, flip it horizontally and then combine those. But there remains a seam, no matter how I snap the two together. 
Someone on an unofficial Affinity Discord Server (credits to gromofdoom) helped me out by saying the snapping was never really working in this software and I need to overlap the two halves, combine them and then delete the unneeded nodes. 
Why does Affinity make such a simple task this painful? That's a pretty difficult workflow for something that wants to be an Adobe alternative.
Or am I blind and there's actually a better way to do that? I attached my project file (with extended history in it!) so you can see what I did (there's much stuff I did which didn't make any sense, lol).
shuriken.afdesign

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The Curve snapping: nodes and control handles video tutorial explains how each of the Node Tool's "Snap" options on the context toolbar work. As mentioned at around 0:40 in the video these snapping options are completely independent of the "global" snapping options on the main toolbar.

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