R: count distinct IDs where selected column is non-null

I have the following dataframe:

user_id <- c(97, 97, 97, 97, 96, 95, 95, 94, 94)
event_id <- c(42, 15, 43, 12, 44, 32, 38, 10, 11)
plan_id <- c(NA, 38, NA, NA, 30, NA, NA, 30, 25)
treatment_id <- c(NA, 20, NA, NA, NA, 28, 41, 17, 32)
system <- c(1, 1, 1, 1, NA, 2, 2, NA, NA)

df <- data.frame(user_id, event_id, plan_id, treatment_id system)

I would like to count the distinct number of user_id for each column, excluding the NA values. The output I am hoping for is:

      user_id   event_id    plan_id   treatment_id  system
  1   4         4           3         4             2

I tried to leverage mutate_all, but that was unsuccessful because my data frame is too large. In other functions, I’ve used the following two lines of code to get the nonnull count and the count distinct for each column:

colSums(!is.empty(df[,]))
apply(df[,], 2, function(x) length(unique(x)))

Optimally, I would like to combine the two with an ifelse to minimize the mutations, as this will ultimately be thrown into a function to be applied with a number of other summary statistics to a list of data frames.

I have tried a brute-force method, where make the values 1 if not null and 0 otherwise and then copy the id to that column if 1. I can then just use the count distinct line from above to get my output. However, I get the wrong values when copying it into the other columns and the number of adjustments is sub optimal. See code:

binary <- cbind(df$user_id, !is.empty(df[,2:length(df)]))
copied <- binary %>% replace(. > 0, binary[.,1])

I’d greatly appreciate your help.

sapply(df, function(x){
    length(unique(df$user_id[!is.na(x)]))
})
#     user_id     event_id      plan_id treatment_id       system 
#           4            4            3            3            2 

aggregate(user_id ~ ind, unique(na.omit(cbind(stack(df), df[1]))[-1]), length)
#           ind user_id
#1      user_id       4
#2     event_id       4
#3      plan_id       3
#4 treatment_id       3
#5       system       2

df %>%
    mutate(key = user_id) %>%
    pivot_longer(!key) %>%
    filter(!is.na(value)) %>%
    group_by(name) %>%
    summarise(value = n_distinct(key)) %>%
    pivot_wider()
## A tibble: 1 x 5
#  event_id plan_id system treatment_id user_id
#     <int>   <int>  <int>        <int>   <int>
#1        4       3      2            3       4

library(dplyr)
df %>% summarise(across(.fns =  ~n_distinct(user_id[!is.na(.x)])))

#  user_id event_id plan_id treatment_id system
#1       4        4       3            3      2

> setDT(df)[, lapply(.SD, function(x) uniqueN(user_id[!is.na(x)]))]
   user_id event_id plan_id treatment_id system
1:       4        4       3            3      2

   apply(df, 2, function(x){length(unique(df[!is.na(x), 1]))})