High-precision direction-of-arrival (DOA) estimation, as a key sensing capability for 6G-enabled applications such as autonomous driving and extended reality, is increasingly dependent on the effective exploitation of spatial degrees of freedom (DOFs). This paper integrates two frontier DOFs-oriented paradigms and proposes a fluid antenna-enabled hybrid analog-digital (FA-HAD) architecture, which features an extremely lightweight front-end configuration mechanism and efficient spatial DOFs exploitation. Within this architecture, a collaborative spatial-phase sampling strategy is first developed to enable real-time 2-D DOA estimation under compressive observations, and a single-source CRLB analysis is provided to quantify the achievable performance limit, offering quantitative guidance for accuracy-overhead trade-offs. Furthermore, an efficient virtual-array spatial covariance matrix reconstruction method is proposed to recover a physically meaningful covariance representation, thereby providing a covariance-domain interface that is directly reusable by a broad class of existing covariance-based array processing and array design techniques, which strengthens the scalability and transferability of the proposed architecture. Building upon the reconstructed SCM, a Jacobi-Anger expansion based dimension-reduced MUSIC estimator is further derived for arbitrary planar arrays with a favorable computational cost. Simulation results demonstrate that the proposed FA-HAD framework attains DOA accuracy close to fully digital systems while substantially reducing RF hardware complexity and training overhead.