he logical error rate increases with m
If you run for longer, there's more time for errors to occur. You need to do a conversion of the per-shot error rate to a per-round error rate or per-$d$-round (per-quop) error rate, e.g. using
sinter.shot_error_rate_to_piece_error_rate, if you want to compare different numbers of rounds. Also you want enough rounds to amortize away boundary effects from the start and end of the experiment; like $3 \cdot d$ or $4 \cdot d$ rounds.
I found that the threshold decreases as m increases
You need to use larger values of $d$. If your error unit is a number of rounds linear in $d$, you will see the crossing point where different noise strengths have the same logical error rate vary a lot with $d$ when $d$ is small. For example, when using $r=2d$ the $d=5$ experiment is nearly twice as long as the $d=3$ experiment, whereas the $d=31$ experiment is basically the same length as the $d=29$ experiment.
In any case the threshold is the wrong number to estimate. The threshold is where the code doesn't work; you want to know numbers where the code does work. Behavior near threshold is qualitatively different from behavior well below threshold, where quantum computers will actually run. If you focus on near-threshold behavior, you will learn the wrong lessons about what works well and what works poorly.