Parabolic Stochastic Partial Differential Equations (SPDEs) are fundamental tools for modelling spatiotemporal phenomena where a deterministic system is perturbed by random noise. Often, this noise is assumed to be white in time and colored in space, with its spatial covariance $Q$ specified parametrically, e.g., from the Mat\'ern class. Nonparametric estimation and validation of these covariance structures, especially when the differential operator $A$ of the SPDE is unknown, is a challenging area and existing research often focus on parametric estimation. This work addresses the nonparametric estimation of the trace-class noise covariance operator $Q$ (or its kernel $q$) for linear parabolic SPDEs of the form $\dd X_t + A X_t = \dd W_t$ on a bounded domain $\mathcal{D} \subset \mathbb{R}^d$. The core of the methodology lies in an asymptotic theory for the infinite-dimensional realized covariation, $RV_t^{\Delta,O} = \sum (O X_{i\Delta}-O X_{(i-1)\Delta})^{\otimes 2}$, derived from discrete space-time observations with temporal resolution $\Delta$ and a spatial observation operator $O$. Various spatial sampling schemes are considered, including continuous sampling, local averages, and pointwise evaluation. Under space-time infill asymptotics ($\Delta \to 0$ and spatial resolution $h \to 0$), it is established that $RV_t^{\Delta,O}/t$ is a consistent estimator of $Q$ in the Hilbert-Schmidt norm, requiring only mild regularity assumptions on $Q$. Rates of convergence are provided, highlighting the interplay between spatial and temporal data density. Furthermore, central limit theorems for the estimator are derived. A key application of this theory is the construction of asymptotic goodness-of-fit tests for hypothesized noise covariance structures $Q_0$. These results provide a robust framework for noise covariance analysis in SPDEs, particularly relevant in practical settings where model parameters are uncertain. This is joint work with Dennis Schroers, University of Bonn.