How to interpret parameters in brm with family=Gamma

Question

I have a question about interpretation for a bayesian model with a gamma distributed dependent variable.

I have a dataset containing 3 groups’ sentiment score data, from 0 to 4 (this is a continuous variable), and my goal is to determine if there is an effect by group.

After following many online tutorials, I settled on a gamma score (did LOO of different families) - model below:

This is what R returns for my BRM:

 Family: gamma 
Links: mu = inverse; shape = identity
Formula: sentiment ~ group + (1 | id)
Data: df (Number of observations: 1856)
Samples: 20 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 20000

The output is as follows:

Group-Level Effects: 
~id (Number of levels: 1856) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.40      0.16     0.04     0.65 1.01     2289     2424

Population-Level Effects: 
            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept       2.55      0.09     2.38     2.74 1.00     6787    13508
group           1.22      0.14     0.95     1.50 1.00    27476    15066
group  .        1.29      0.15     1.00     1.58 1.00    24998    15147

Family Specific Parameters: 
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
shape     1.65   [![enter image description here][1]][1]   0.06     1.54     1.76 1.00     7659    11316

So group 2 and 3 are different in sentiment to group 1 (as 95%CI don’t cross 0) but how do I interpret the estimate? Do I need to log? Transform something? How would I make this into a sentence? I’m confused as when I plot the conditional effects, I don’t understand what is on the y axis? Attached is the plot.

Thank you for your patience in helping me to understand!