  The footprint of LoTSS-DR2 covers 309 PSZ2 galaxy clusters, 83 of which host
a radio halo and 26 host a radio relic(s). It provides us an excellent
opportunity to statistically study the properties of extended cluster radio
sources, especially their connection with merging activities. We aim to
quantify cluster dynamic states to investigate their relation with the
occurrence of extended radio sources. We also search for connections between
intracluster medium (ICM) turbulence and nonthermal characteristics of radio
halos in the LoTSS-DR2. We analyzed XMM-Newton and Chandra archival X-ray data
and computed concentration parameters and centroid shifts that indicate the
dynamic states of the clusters. We also performed a power spectral analysis of
the X-ray surface brightness (SB) fluctuations to investigate large-scale
density perturbations and estimate the turbulent velocity dispersion. The power
spectral analysis results in a large scatter density fluctuation amplitude. We
therefore only found a marginal anticorrelation between density fluctuations
and cluster relaxation state, and we did not find a correlation between density
fluctuations and radio halo power. Nevertheless, the injected power for
particle acceleration calculated from turbulent dissipation is correlated with
the radio halo power, where the best-fit unity slope supports the turbulent
(re)acceleration scenario. Two different acceleration models, transit-time
damping and adiabatic stochastic acceleration, cannot be distinguished due to
the large scatter of the estimated turbulent Mach number. We introduced a new
quantity $[kT\cdot Y_X]_{r_\mathrm{RH}}$, which is proportional to the
turbulent acceleration power assuming a constant Mach number. This quantity is
strongly correlated with radio halo power, where the slope is also unity.
