Confidence intervals for each grouping factor in glmmTMB model

I'm treating a data with one continuous variable and one categorical variable. I built a model as following using glmmTMB:

m=glmmTMB(y~x+(1+x|group), family=Gamma(link="log"), data=dat)

'group' is the categorical variable with 20 levels and I want to calculate the confidence interval for each group considering both fixed and random slope. Now I have two questions:

1. Is it plausible to calculate CIs for each group in a model with random slope?
2. If it's okay, how can I implement that?

So far I tried confint() but both seemed something is wrong.

confint(m, method="profile")
                        2.5 %      97.5 %
(Intercept)        3.47032911  3.62824116
x                  0.03020511  0.06036813
theta_1+x|group.1 -1.85226484 -1.30972404
theta_1+x|group.2 -3.74515169 -3.04747076
theta_1+x|group.3 -0.14530387  0.83050143

Although group is the variable with 20 levels, only 3 is showed here and their names are dropped.And I also tried parametric bootstrapping with chatGPT's help.

for(i in 1:nboot){

  sim_data <- simulate(m)[[1]]
  dat_boot <- m$frame
  dat_boot$y <- sim_data

  m_boot <- try(glmmTMB(y ~ x + (1+x|group),
                         family=Gamma(link="log"), data=dat_boot), silent=TRUE)
  if(!inherits(m_boot, "try-error")){
    fix_boot <- fixef(m_boot)$cond["x"]
    ranef_boot <- ranef(m_boot)$cond$plot[,"x"]
    boot_slopes[i, ] <- fix_boot + ranef_boot
  }
}

ci <- apply(boot_slopes, 2, function(x){
  quantile(x, probs = c(0.025, 0.975), na.rm=TRUE)
})
print(ci)

I checked the result but I highly suspect something is wrong, especially the grouping structure is lost because the CIs are too homogenic/similar among groups(seeing my row data, I believe they shouldn't).

I don't cling to glmmTMB, but fitting is somehow better with this than lme4.

There is both a statistical question and a computational question here.

The statistical question is "can I get confidence intervals on expressions involving a random effect?" The answer is, "it depends whether you're a frequentist or not, and how rigorous you want to be". According to a frequentist, random effects are not parameters, so they (and expressions involving them) don't have confidence intervals. However, we can get prediction intervals, or intervals combining the sampling distribution of the parameters with the conditional distributions of the random effects ...

There is an implementation for lme4 here and for glmmTMB here (I realize this violates the "link-only answer" rule, I will try to come back later and copy the content here ...)