A comprehensive spectroscopic map of the electronic, magnetic, and lattice excitations is presented for the bilayer nickelate La₃Ni₂O₇ using Raman scattering at ambient pressure. Upon entering the spin density wave state below 153 K, the A_1g channel exhibits an abrupt electronic spectral gap with a clear isosbestic point. In contrast, the B_1g and B_2g channels are dominated by pronounced two-magnon (2M) excitations, representing a signature of incipient Mottness. These 2M signals in both channels constitute evidence for two distinct in-plane spin exchange interactions along the Ni-O bonding and its diagonal directions. Calculations based on the spin wave theory further reveal that the 2M mode in the B_2g channel arises from the competition between two bond-diagonal antiferromagnetic interactions mediated by nickel d_(x²-y²) orbitals. Furthermore, emergent low-energy 2M excitations below 10 meV are found to originate from distinct, weaker spin moments, supporting spin disproportionation. Simultaneously, an anomalous softening of B_1g phonons from 280 down to 4.5 K is uncovered, suggesting the presence of an incipient lattice instability leading to checkerboard-type breathing modulations. Collectively, these findings identify a ground state of the bilayer nickelate characterized by competing bond-diagonal interactions, spin disproportionation, and an incipient lattice instability, establishing key ingredients for understanding the mechanism of nickelate superconductivity.