Geoengineering refers to any attempt to engineer the planet. It isn't just aerosol injection, but would also include solar shades, dumping iron in the ocean, modifications to forest cover, creation or destruction of biomes (e.g., turning the Sahara back into something other than a desert), and in the future, conceivably things like bioengineering species to obtain desired goals (e.g., consider a plant we could farm that somehow sequestered CO2 in a form we could more easily bury). It's the terrestrial equivalent of the term "terraforming".

That's not at all my understanding eg. https://en.wikipedia.org/wiki/Geoengineering

'chemtrails' does not appear in the article.

Of course it does not, because "chemtrails" officially do not exist. They call it "stratospheric aerosol injection".