The Back-n white neutron facility at the China Spallation Neutron Source (CSNS) provides neutrons in the 0.3 eV–300 MeV energy range, serving as a crucial platform for neutron-induced nuclear reaction studies in China. With a flight length of about 76 m, neutrons in Endstation 2 show excellent neutron energy resolution, providing ideal conditions for experiments such as neutron capture cross-section measurements relevant to astrophysical nucleosynthesis and key nuclear data. Neutron capture reactions are measured mainly using low- to intermediate-energy neutrons (below 1 MeV), and the precision of experimental results strongly depends on the neutron energy spectrum in this energy range. Due to the stable operation of the CSNS, the neutron energy spectrum of Back-n remains highly stable over extended periods, but it also evolves with structural adjustments of the CSNS's components such as the target and beam window. In this work, the ⁶Li-Si beam monitor at Back-n Endstation 2 is used to measure the low- to intermediate-energy neutron spectrum under the 50-15-40 collimator configuration in different periods. Relative neutron energy spectra in the 0.3 eV–1 MeV range (100 bpd (bin per decade)) are obtained before and after the proton beam window replacement in 2024 and the target structure adjustment in 2025. The unfolding threshold is extended down to 10 eV, achieving a total uncertainty of 1%–6.8%. The results indicate that the new proton beam window reduces the neutron flux intensity in the eV to keV energy range and significantly changes the spectral shape, whereas adjustments to the target slightly increase the neutron flux intensity in the eV to keV range and marginally modify the spectral shape. Additionally, by analyzing the neutron energy spectra under two different commonly used collimator configurations, the comparisons are also made of the differences in their spectral shapes. The datasets presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00213.00214.