In line with the Paris Agreement and the United Nations Sustainable Development Goals, the use of fossil fuels is to be phased out in the coming decades. Fossil-free hydrogen is a promising candidate for decarbonising the energy sector. However, hydrogen combustion is known to produce undesirable emissions such as nitrogen oxides (NOx) and calls for mitigation measures such as steam-diluted hydrogen combustion, which is known to reduce the NOx emissions. This study focuses on improving the understanding of NOx formation in a swirl-stabilised, steam-diluted, non-premixed hydrogen/air combustion using high-fidelity large eddy simulation (LES) and zero-dimensional (0D) perfectly stirred reactors (PSR). The LES results are used to identify four salient points in the domain where the NOx chemistry is analysed in detail. These points are chosen in the main flame, flame tail, post-flame and central recirculation regions. Note, the high heat release rate (HRR) region is referred to as the main flame while the flame tail denotes the low-HRR and V-shaped flame region adjacent to the main flame. Based on the LES data at these chosen points, the contribution of the major NO production pathways such as the Zeldovich mechanism, extended Zeldovich mechanism, N2O route and the NNH route are studied and reveal different rates of production of NO (i.e. ROPNO). Also, the role of individual reactions in NO production and consumption is investigated. Furthermore, reaction pathway diagrams illustrating the chemical pathways leading to NO are visualised. The sensitivity of NO to each reaction is also reported. These analyses provide insights into the NO chemical pathways observed at the salient points across the domain. The dominance of the Zeldovich mechanism remains but is much less compared to that in dry hydrogen combustion as its contribution to ROPNO is less than 20% at all the points considered. However, the extended Zeldovich mechanism is significant at all the points. The NNH route is observed to be important in the flame regions. The major NNH reaction contributing to ROPNO in the flame regions is NNH+O⇌NH+NO. Furthermore, the complex NO chemistry at all the identified points is presented in great detail using the above-mentioned analyses and illustrations. This work highlights the possibility of combining a high-fidelity simulation and a simple 0D ideal reactor to decipher the nuances of NO chemical pathways in a practical swirl-stabilised gas turbine combustor and provide new understanding for assisting engineers in designing clean burners.