  The manipulation fidelity of a single electron qubit gate-confined in a
$^{28}$Si/SiGe quantum dot has recently been drastically improved by nuclear
isotope purification. Here, we identify the dominant source for low-frequency
qubit detuning noise in a device with an embedded nanomagnet, a remaining
$^{29}$Si concentration of only 60$\,$ppm in the strained $^{28}$Si quantum
well layer and a spin echo decay time $T_2^{\text{echo}}=128\,\mu$s. The power
spectral density (PSD) of the charge noise explains both the observed
transition of a $1/f^2$- to a $1/f$-dependence of the detuning noise PSD as
well as the observation of a decreasing time-ensemble spin dephasing time from
$T_2^* \approx 20\,\mu$s with increasing measurement time over several hours.
Despite their strong hyperfine contact interaction, the few $^{73}$Ge nuclei
overlapping with the quantum dot in the barrier do not limit $T_2^*$, as their
dynamics is frozen on a few hours measurement scale. We conclude that charge
noise and the design of the gradient magnetic field is the key to further
improve the qubit fidelity.
