Thanks for your replies!
And, Unterwegs, thanks for your table of interline carrier agreements. I could have been able to find it myself, as I see it comes from KVS tool that I use as well.

Thing is, I asked at OS Facebook page about checking luggage through, and they gave me the following answer:
unfortunately it's not possible to check the luggage all the way to Taipei in your case, because your continuation flight is not operated by a Star-Alliance Carrier. So you need to check-in your luggage again in BKK. We wish you a good flight though!

I have more trust in your chart than in this 'official' OS reply...