Battle bots are not exactly robotics, they’re RC cars with extra servo channels. Personally I find them boring compared to FPV, but the entry is pretty much the same - watch YouTube tutorials. You could find a book but anything you’d find there would be outdated, unless you need the absolute basics like Kirchhoff's circuit laws - which are as useful for building stuff as set theory is useful for writing wrappers for REST APIs.. just don’t connect negative to positive and you should be fine:)
You might learn Fusion if you want to 3D model the chassis - again, everything is on Youtube.
You /can/ totally do it hardmode though. I did small plastic battlebots several years ago, and I went for Xbee teleop communication to a microcontroller, controlling PWM motor drivers etc. (no, didn't go far enough that this gave me any competitive advantage)
But my real passion is tying together servos/microcontrollers/motors letting me make custom built teleop'd quadrupeds with airsoft guns, lasers and cameras...
There's a lot of stuff you can do in robotics before you get to true autonomy.
(just rambling, inspired by your comment; nothing you said is wrong :) )
You might learn Fusion if you want to 3D model the chassis - again, everything is on Youtube.
Good luck!