Answering a couple of parts of my own question after looking at the R source:
First, the info is stored in the sampler_params attribute of @sim$samples (from the get_sampler_params method).
Second, apparently the 4th chain is the only one with big tree depths:
> xt <- rstan:::.sampler_params_post_warmup(fit4, "treedepth__", as.df=TRUE)
> summary(xt)
iterations chain:1 chain:2 chain:3 chain:4 chain:5
Min. :1001 Min. :6 Min. :6 Min. :6 Min. : 5.00 Min. :6
1st Qu.:1251 1st Qu.:6 1st Qu.:6 1st Qu.:6 1st Qu.:10.00 1st Qu.:6
Median :1500 Median :6 Median :6 Median :6 Median :12.00 Median :6
Mean :1500 Mean :6 Mean :6 Mean :6 Mean :11.23 Mean :6
3rd Qu.:1750 3rd Qu.:6 3rd Qu.:6 3rd Qu.:6 3rd Qu.:13.00 3rd Qu.:6
Max. :2000 Max. :6 Max. :6 Max. :6 Max. :15.00 Max. :6
chain:6 chain:7 chain:8 chain:9 chain:10
Min. :6 Min. :6 Min. :6 Min. :6 Min. :6
1st Qu.:6 1st Qu.:6 1st Qu.:6 1st Qu.:6 1st Qu.:6
Median :6 Median :6 Median :6 Median :6 Median :6
Mean :6 Mean :6 Mean :6 Mean :6 Mean :6
3rd Qu.:6 3rd Qu.:6 3rd Qu.:6 3rd Qu.:6 3rd Qu.:6
Max. :6 Max. :6 Max. :6 Max. :6 Max. :6
The 4th chain also has a slightly larger stepsize than the others (0.0982; next closest is 0.0945, with values ranging down to 0.066).
I still don’t know why the middle panel shows blue and green for treedepth > 6 while the others show only green.
P.S. Is there a way to get a fixed width font?