automate ggplots while using variable labels as title and axis titles

I'm getting a bit mixed up with NSE and a plot function. I'm trying to automate plotting a few plots at once while labeling axis etc. using variable labels (not names). Lets say we have a large dataset with all variables already labelled. Small example here:

library(tidyverse)
library(sjlabelled)
library(ggplot2)
library(cowplot)
data("diamonds")
diamonds <- diamonds %>% 
  var_labels(
  cut ="nice cut",
  color = "all colours",
  clarity = "very claity all",
  depth = "test depth")

The basic plot I want is this:

p1 <- ggplot(diamonds, aes(x = cut, y = depth)) + geom_boxplot(aes(fill = cut)) +
  theme_cowplot() + 
  lab(title = "Plot of test depth ~ nice cut",   #based on label variable
                           x = "nice cut",      #based on label variable
                           y = "test depth",    #based on label variable
                         fill = "nice cut")    #based on label variable
p1

I want to automate this plot by cycling through other variables. So I want boxplots of columns in vars separately by depth The following is what I'm trying to do.

#firstly i think i should have labels separately (wondering is there a way I can use them directly from variable label?)

my_labels <-   c(
  cut = "nice cut",
  color = "all colours",
  clarity = "very claity all",
  depth = "test depth"
)

#plot function
plot_f <- function(df, x_var, y_var, x_var_label, y_var_label) {
  ggplot(df, aes(x = {{x_var}}, y = {{y_var}})) + geom_boxplot(aes(fill = {{x_var}})) +
    theme_cowplot() + labs(title = paste("Plot of", {{x_var_label}}, "~", {{y_var_label}}),
                           x = {{x_var_label}},
                           y = {{y_var_label}},
                           fill = {{x_var_label}})
}

#variables to cycle through
vars <- c("cut", "color", "clarity")
plot_list <- vars %>% 
  pmap(~plot_f(diamonds, .x, depth, my_labels)) #need to specify y_var_label & x_var_label, is there a 
#way I can just specify my_labels here?

#Finally plot lists
grid.arrange(grobs = plot_list, ncol = 1)

Other code attempts

Thats the approach I was thinking, I wonder am I better off trying to add the labels later separately as was done here using plot_list$labels?

#Also tried a for loop which worked but the fill didnt (and also missing the variable labels)
p <- list()
for(i in vars){
  p[[i]] <- ggplot(diamonds, aes_string(x = i, y = "depth", fill = i)) + geom_boxplot() +
    #note aes_string instead of aes
    theme_cowplot()
}
grid.arrange(grobs = p, ncol = 1)

EDIT

This simpler version plots but the plot isn't capturing the fill correctly and obviously missing the variable labels (paste etc) I want:

    #plot function
    plot_f <- function(df, x_var, y_var) {
      ggplot(df, aes(x = {{x_var}}, y = {{y_var}})) + geom_boxplot(aes(fill = {{x_var}})) +
        theme_cowplot() 
    }

    plot_f(diamonds, cut, depth )  #plots fine

    #variables to cycle through
    vars <- c("cut", "color", "clarity")

#runs
    plot_list <- vars %>% 
      map(., ~plot_f(diamonds, .x, depth))

    #plots but fill isn't correct
    grid.arrange(grobs = plot_list, ncol = 1)

Any help appreciated.