We investigate the geodesic structure, optical response, and thermodynamic fluctuations of a Schwarzschild-like black hole solution in bumblebee gravity in the presence of two topological defects: a global monopole and a cloud of strings. Working directly with the effective line element, we derive the null and timelike geodesic equations and analyze circular photon orbits, critical impact parameters, weak-field deflection, shadow relations, observational shadow constraints, and the innermost stable circular orbit (ISCO). We then formulate the thermodynamics using a properly normalized Killing time at infinity, obtaining the Hawking temperature, entropy, the first-law-compatible thermodynamic energy, the heat capacity, and the Helmholtz free energy in the normalized frame. Finally, we examine thermodynamic fluctuations through Ruppeiner information geometry by allowing the monopole scale to fluctuate macroscopically while keeping the string-cloud sector fixed. The first-law-compatible two-parameter state space has a nontrivial scalar curvature, which is negative in the physical domain and does not develop a finite degeneracy locus. We comment on the importance of using the energy conjugate to the normalized Killing time and on possible extensions in which additional thermodynamic variables, such as charge or pressure, are promoted to fluctuating degrees of freedom.
Publication Date: 2026-06-19