Thank you for the link.
Soft power is very hard to project without some sort of legitimacy granted by the projectee. For example, Iran and North Korea and Cuba are virtually incapable of projecting soft power in the West, because all channels for doing so have been blocked through various form of sanctions.
The likes of Russia, Saudi Arabia, Qatar... all have been granted legitimacy to one extent or another by the UK government and the European Union, to the extent that they can attempt to project soft power through cultural institutions (of which sport is one channel), but that legitimacy is the sticking point for me.
As this episode with Ukraine has shown, soft power doesn't really do you good once legitimacy is stripped away. Sponsorships by Russian institutions have been canceled. They're being kicked out of international sport. If Saudi Arabia was to invade, instead of Yemen, an innocent country like Israel, it's sponsorship of Newcastle would do it no good and they probably would be forced to sell. Which begs the question as to what benefit sportswashing brings beyond financial means (taking the link you provided as fact, the needle doesn't really move that much for Qatar/Saudi, and if it did, that's your sustainability argument right there for FFP).
Finally, you've admitted the term sportswashing doesn't really apply to Abramovich... Which is one of my main points, that it's not a term that has a clear definition and is applied consistently, if major outlets/journalists can incorrectly use the term. Money laundering has a clear definition and it's very simple to identify. Sportswashing is deliberately ambiguous.