How can I show significant comparisons from Tukey post-hoc test in ggplot2 bar plot?

Question

I have a dataset with several variables that looks like this:

    Competitor Disturbance  Group     MT       CVt
1           M           P       A   17.416667  63.39274
2           M           P       A   11.055556  91.32450
3           M           C       N   13.928571  78.11438
4           B           C       N   13.500000  61.20542
5           B           T       E   12.700000  48.11819
6           B           T       E   27.250000  63.44356

I've made a GLMM (mMT1) with 3 predictors (Competitor, Disturbance and Group), one response (MT) and one random factor (Species, not shown in example dataset).

After fitting and checking the model, I calculated ls means with the package emmeans:

ls_MT <- emmeans(mMT1, pairwise~Disturbance*Competitor*Group, type="response")

And performed a post-hoc test:

post_MT  <- emmeans(mMT1, transform="response", component="cond",list(~Disturbance|Competitor|Group,~Competitor|Group|Disturbance,~Group|Disturbance|Competitor))
pairs(post_MT)

Finally I produced a bar chart with ggplot2, based on the ls means and se

ggplot(ls_MT, aes(x=Disturbance, fill=Competitor, y=response))+
  geom_bar(stat="identity",position=position_dodge())+
  facet_grid(cols=vars(Group))+labs(y = "log10(MT)")+
  scale_color_manual(values=c("#2ca02c","#d62728"))+
  geom_errorbar(aes(ymin=ls_MT$lower, ymax=ls_MT$upper), width=.2,
                position=position_dodge(.9))+
  theme_light()

Which produces a plot like this:

At this point I'm struggling with 2 things:

1. Is there a way to have the bar plots side by side without the faceting by group? It looks ok but I'd prefer them to be one single plot rather than 3 side by side

2. How can I annotate on the graph the comparisons from the post-hoc test? I've seen that several functions allow to perform separate tests (e.g. stat_compare_means) and plot those results, but I can't find a solution for Tukey's post-hoc test. Another solution could be to add

     geom_signif(map_signif_level = c(" * * * "=0.001, " * * "=0.01, "*"=0.05), comparisons = list(c("P","C"),c("P","T"),c("C","T"))
   

but that pools together the B and M (Competitor) values of each Disturbance (P, T, C). In this case I'd actually like to compare the B and M within each of P, T and C. Or even better, how can I specify between which bars I'd like to show the results of the post-hoc? For example I'd like to compare A-T-B with E-T-B, etc.