The LOw-Frequency ARray (LOFAR) provides a unique opportunity to probe the magneto-ionised structure of our Galactic neighbourhood with great resolution. In this work, we present a new mosaic created with the second release of LOFAR Two-Metre Sky Survey data (LoTSS-DR2), which probes polarised synchrotron emission in the high-latitude inner Galaxy. This is the third paper in a series whose main goal is understanding the LOFAR Faraday tomographic data at low radio frequencies and utilising it to explore the intricate structure of the local interstellar medium (ISM). Our objective is to characterise the observed emission through multi-tracer analysis to better understand the volume and the structures that may be observed with LOFAR. Furthermore, we exploit Faraday depth as a unique tool to probe the diffuse magnetised structure in the local ISM. We produce a mosaic Faraday cube of LoTSS-DR2 data by applying a rotation measure synthesis algorithm. From the cube, we construct Faraday moment maps to characterise the nature of spectra. Additionally, we quantify the linear depolarisation canals using the Rolling Hough transform and use them to search for alignment with other data sets. Utilising LoTSS-DR2 observations alongside complementary data sets including Planck polarisation data, HI emission maps and starlight polarisation measurements, we explore conditions along observed lines of sight and estimate the distance to the Faraday structures. The Faraday cube reveals a remarkably ordered structure across two-thirds of the observed area, whose orientation aligns well with that of both the HI filaments and the magnetic field. We estimate the minimum distance to the Faraday structures to be between 40 and 80 pc, which puts them in the vicinity of the Local Bubble wall. The emission is organised in a large gradient in Faraday depth whose origin we associate with the curved wall of the Local Bubble. Comparing our data with a model of the Local Bubble wall, we conclude that we might be probing a contribution of the medium inside the Local Bubble cavity as well, corresponding to the complex of local interstellar clouds. Moreover, we propose a toy model incorporating an ionised front of finite thickness into the Local Bubble wall, as a curved, cold neutral shell alone is insufficient to produce the observed gradient. We explore possible magnetic field strengths, as well as the possible distribution of the neutral and ionised medium inside the wall, within the constraints of the observed Faraday depth.

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