Sometimes technological difference can be so great the question is not "if" the Culture would win rather "how it feels like" winning. As in aesthetically.
You can kill everything with replicated weapons just made out of the free material out of a single asteroid like Psyche. Yet they'd probaly find it too ugly/brutish.
You can have nanobots that first slowly infect everything and then simultanously disconnect every brainstem at the same time. Thats in a way is much more "humanitarian" since humans dont get to realize they are getting invaded or feel fear about losing etc.
But ultimatly as
>>64227591 said at this level the way I imagine a "touchy feely" civilization (but that is also proud of itself rather than self-hating like some turbo leftists/rightist today) would just go for a form of slow assimilation. As well as to avoid maybe the ethics that this is too foreful "brainwashing" rather making it feel more like it was your idea all along.
The Culture is pretty much immortal compared to humanity and has all the time in the world and work in timescales far larger than individual human politiicans and generation. It could even do it slowly in a way that it almost looks like "natural" evolution and social/technological development.
Its just would so happen that after 2000 years, humans would just happen to be indistinct from Culture citizens in bodies and morality. And since they would be indistinct even when told afterwards what has been done, they will just agree and say "oh year, obviously that was the most humanitarian option and obviously the Culture is great. Thanks for not killing us" and then plug into it straight away.