spread_draws() for a coef() metric

[ASKurz]

I'd like to use spread_draws(), or some other function if more appropriate, to pull parameters in a coef() metric (i.e., population mean + random effect). I can do it, but the code seems clunky and I'm wondering if there's a more elegant way. Here's an example of what I mean.

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

# Load the data
data(ChickWeight)

# Adjust the data
cw <- ChickWeight |> 
  data.frame() |> 
  rename_all(.funs = tolower) |> 
  mutate(time_z = (time - mean(time)) / sd(time),
         weight_z = (weight - mean(weight)) / sd(weight))

# Fit a model with several random effects
my_fit <- brm(
  data = cw,
  weight_z ~ 1 + time_z + I(time_z^2) + (1 + time_z + I(time_z^2) | chick),
  prior = prior(normal(0, 1), class = Intercept) +
    prior(normal(0, 1), class = b) +
    prior(exponential(1), class = sd) +
    prior(exponential(1), class = sigma) +
    prior(lkj(2), class = cor),
  cores = 4, seed = 1
)

# Extract the posteriors, wrangle, and plot
beta_levels <- c("Intercept", "time_z", "Itime_zE2")
beta_labels <- str_c("beta[", 0:2, "]")

my_fit |> 
  spread_draws(b_Intercept, b_time_z, b_Itime_zE2, r_chick[chick, ranef] | ranef) |>
  # 50 chicks is overkill
  filter(chick <= 10) |>
  pivot_longer(cols = c(b_Intercept:b_Itime_zE2, Intercept:time_z), names_to = "beta") |> 
  mutate(type = ifelse(str_detect(beta, "b_"), "fixef", "ranef"),  # This line is not needed, but can bring conceptual clarity
         beta = str_remove(beta, "b_"),
         chick = factor(chick)) |>
  group_by(.draw, chick, beta) |> 
  summarise(value = sum(value)) |> 
  mutate(beta = factor(beta, levels = beta_levels, labels = beta_labels)) |> 
  
  ggplot(aes(x = value, y = chick)) +
  stat_pointinterval(.width = 0.95,
                     linewidth = 1/4, size = 1) +
  facet_wrap(~ beta, labeller = label_parsed, nrow = 1)

Any thoughts on better versions of the spread_draws() part of the code for combining the fixed and random effects?