The field of compact optical microcavities has received significant research in the past decades, and a broad range of cavity-based micromechanical sensors has been demonstrated. The present approach replaces the frequently employed, complex etched cantilever and membrane structures with a simple thin-film system based on a compressible photonic microcavity to achieve pressure-sensitive wavelength shifting of resonant modes. The effects of a topological dielectric mirror architecture on the light propagation in the system are extensively investigated. Topologically improved light-matter interaction is experimentally demonstrated for systems where thin-film devices are mounted on one side of the photonic cavity due to mechanical constraints. Coupled topological states are examined under the aspect of mode splitting and exhibit advantageous splitting tunability compared to non-topological systems. The findings are complemented by the proposal of a simple spectral evaluation method allowing significant improvement in the precision of integrated Fabry-Pérot sensors. The readout concept of the presented sensor allows a scalable improvement of the measurement precision by evaluating the resonant-mode order in the deformable cavity. The experimental results and conceptual advancements provide pathways for significant improvements addressing the efficiency of light-matter interaction in Fabry-Pérot cavities and the readout precision of sensors incorporating thin-film photodiodes in multimode photonic cavities.