Where does the energy required for excitation of electrons in hybridization come from? We're commonly taught that when atoms want to hybridize in for instance methane, an electron is excited from $2s$ to $2p$ to allow for four unpaired electrons, which is necessary for bonding.

Where does the energy for this excitation come from?
Ab initio hybridisation is a concept taught in schools to help understand how carbon with its one s- and three p-orbitals can achieve a tetrahedral environment. As part of this process, it is required to formally excite an electron.

Formally is the key word here. The entire process is a formal process that has practically nothing to do with real-life atoms (especially because these real-life atoms rather rarely end up in a vacuum without anything around them as the theory assumes). Thus, in real life this formal energy is not needed.