Spectral computed tomography (CT) with photon-counting detectors holds immense potential for material discrimination and tissue characterization. However, under ultra-low-dose conditions, the sharply degraded signal-to-noise ratio (SNR) in energy-specific projections poses a significant challenge, leading to severe artifacts and loss of structural details in reconstructed images. To address this, we propose FSP-Diff, a full-spectrum prior-enhanced dual-domain latent diffusion framework for ultra-low-dose spectral CT reconstruction. Our framework integrates three core strategies: 1) Complementary Feature Construction: We integrate direct image reconstructions with projection-domain denoised results. While the former preserves latent textural nuances amidst heavy noise, the latter provides a stable structural scaffold to balance detail fidelity and noise suppression. 2) Full-Spectrum Prior Integration: By fusing multi-energy projections into a high-SNR full-spectrum image, we establish a unified structural reference that guides the reconstruction across all energy bins. 3) Efficient Latent Diffusion Synthesis: To alleviate the high computational burden of high-dimensional spectral data, multi-path features are embedded into a compact latent space. This allows the diffusion process to facilitate interactive feature fusion in a lower-dimensional manifold, achieving accelerated reconstruction while maintaining fine-grained detail restoration. Extensive experiments on simulated and real-world datasets demonstrate that FSP-Diff significantly outperforms state-of-the-art methods in both image quality and computational efficiency, underscoring its potential for clinically viable ultra-low-dose spectral CT imaging.