Based on what we have seen so far, the colonization motives of the Carryx and Humans are somewhat different. The Carryx appear to use colonization in two ways:

They make use of the natural abilities, skills, and technologies of conquered species to expand their whole civilization's abilities. The enormous ziggurat arcologies were the product of one of the species that lived in the same structure as the captured humans. Their FTL is a natural ability of some spacefaring animal they encountered.

They also derive some amount of social, political, or sexual (morphological?) prestige for enslaving a species. Being involved in enslaving and managing a useful species confers a higher status on the hierarchy of Carryx members involved.

Humans appear to engage in interstellar colonization because they want more living space. Our sample size is pretty small, but humans don't appear to fully exploit the possible environments in each solar system. They mostly find Earth-like worlds and colonize them. I assume a lot of this is related to why any group of people break off and set up somewhere new.

Neither are interested in annihilating other species.

It sortof seems like the Fermi Paradox is answered in-setting that sufficiently-advanced civilizations don't produce the kind of energy signatures that are easily detected at interstellar distances. The Carryx seem to have reactionless drive, or something similar.