compare_levels() for pairwise standardized mean differences

[ASKurz]

I have a Gaussian DV with 3+ groups. I'd like to compare the means with a standardized mean difference (SMD, like a Cohen's d), but standardized with pairwise pooled SDs, rather than the overall pooled SD. I think the nicest way to do this is to use compare_levels() twice, first for the raw mean contrasts, and then second to compute the pairwise pooled SDs. Then I can combine the two to compute the pairwise SMDs. Is this the preferred approach, or can you see a better alternative?

# Load
library(tidyverse)
library(brms)
library(tidybayes)

# Make the data
set.seed(3)

dat <- data.frame(
  group = letters[1:3],
  mu = -1:1,
  sigma = 9:11 / 10) |> 
  mutate(y = map2(mu, sigma, .f = \(mu, sigma) rnorm(n = 200, mean = mu, sd = sigma))) |> 
  select(group, y) |> 
  unnest(y)

# dat |> 
#   group_by(group) |> 
#   summarise(m = mean(y),
#             s = sd(y))

# Fit the model
fit <- brm(
  data = dat,
  bf(y ~ 1 + group, sigma ~ 1 + group),
  cores = 4, seed = 1)

# Wrangle
left_join(
  # Mean contrasts
  distinct(dat, group) |> 
    add_linpred_draws(fit, value = "mu") |> 
    compare_levels(variable = mu, by = group),
  # Pairwise pooled SDs
  distinct(dat, group) |> 
    add_linpred_draws(fit, dpar = "sigma", transform = TRUE) |> 
    compare_levels(variable = sigma, by = group, fun = \(a, b) sqrt((a^2 + b^2) / 2)) |> 
    # Adjust the name for the join
    mutate(group = str_replace(group, ":", "-")),
  by = join_by(.chain, .iteration, .draw, group)
) |> 
  # Compute the pairwise SMDs
  mutate(smd = mu / sigma) |> 
  
  # Plot
  ggplot(aes(x = smd, y = group)) +
  stat_halfeye() +
  labs(x = "Mean difference standardized with the pairwise pooled SD",
       y = NULL)