  The unveiling of superconductivity in La$_3$Ni$_2$O$_{7-\delta}$ under
pressure, following the suppression of a high-temperature density wave (DW)
state, has attracted considerable attention. Notably, the nature of this
competing DW order remains elusive, presenting a crucial question that demands
further investigation. Here, we employ the muon-spin rotation/relaxation
($\mu$SR) technique combined with dipole-field numerical analysis to probe the
magnetic response of La$_3$Ni$_2$O$_{7-\delta}$ as a function of hydrostatic
pressure. At ambient pressure, $\mu$SR experiments reveal commensurate static
magnetic order below $T_{\rm N} \simeq 151$K. The comparison of the observed
internal magnetic fields with dipole-field calculations reveals the magnetic
structure's compatibility with a stripe-type arrangement of Ni moments
($\simeq0.3-0.7$$\mu_{\rm B}$), characterized by alternating lines of magnetic
moments and non-magnetic stripes. Experiments under pressure (up to
$p\simeq2.3$~GPa) demonstrate an increase of the magnetic ordering temperature
at a rate ${\rm d}T_{\rm N}/{\rm d}p\simeq 2.8$ K/GPa. This trend is opposite
in sign and significantly smaller in magnitude compared to the changes observed
in the DW order of unknown origin reported by Wang et al. [arXiv:2309.17378].
Our findings reveal that the ground state of the La$_3$Ni$_2$O$_{7-\delta}$
system is characterized by the coexistence of two distinct orders -- the spin
density wave and, most likely, charge density wave -- with a notable
pressure-induced separation between them.
