This paper presents what is, to our knowledge, the first systematic application of Riemannian manifold analysis to the study of dynamical transitions in human EEG covariance structure. Using the affine-invariant metric on symmetric positive-definite matrices, we demonstrate that multichannel EEG covariance evolves through metastable geometric phases (discrete quasi-stable states separated by abrupt transitions) during sustained attention tasks. Across 20 subjects and 40 recording sessions from the publicly available COG-BCI dataset, plus an independent ~60-minute driving simulation, we document heavy-tailed speed distributions (session-level Fisher combined p = 7.32 × 10⁻⁸ across 40 sessions; a more conservative subject-level aggregation gives p = 6.0 × 10⁻⁴), a median 4.0-fold enrichment of effective-rank (dimensionality) changes at transition boundaries (18 of 20 subjects, 90%), and a dissociation between stochastic transition timing and deterministic regime identity consistent with Kramers escape theory. Geometric speed increases with working memory load by an ordered (Jonckheere-Terpstra) trend and correlates modestly with reaction times, establishing functional relevance without circularity. These findings connect to recent geometric analyses of transformer neural networks, suggesting that metastable phase structure may be a convergent computational architecture across biological and artificial information-processing systems. All analyses use publicly available datasets and standard open-source tools. Version 3 (June 2026) corrects citations, statistical reporting, and figure and method descriptions, and removes a circularity in the boundary-enrichment and lane-overlap analyses: the enrichment measure is now the change in effective rank near transitions (rather than the partly circular Riemannian displacement), and the driving-dataset covariance excludes a non-neural vehicle-position channel that earlier versions had inadvertently retained. No qualitative finding changed; full details are in the in-paper Corrigendum.