Is the Kovri project designed to solely benefit Monero or will the codebase be easily usable for all I2P developers?
While developed under the monero project umbrella, Kovri will be usable for general I2P usage, not only for monero. Even when used for monero, it will also be usable for other uses, if the user chooses so. Indeed, the advantage of being usable for general I2P traffic means that an observer seeing you using Kovri (which I assume may be possible via fingerprinting) will not know you are using monero, rather than something else (at least, from looking at the I2P traffic).
I believe the intent of building a separate I2P router was to avoid depending on Java and its libraries, which would have constrained the platforms which could run monero via I2P.