Use of if_else() function in conjunction with group_by, all() and is.na() in R

I searched the forum for a problem similar to mine, but could not find something matching exactly that problem.

I have an R dataframe with a grouping column and columns containing values, such as doubles and date. What I want to do is to write a function that groups the dataframe and create a new column that (1) if the value column contains only na, returns na or (2) if the value column contains at least one non-na, return, say, the maximum. I have attempted the following:

library(dplyr)
a <- c("A", "A", "B", "B", "C", "C")
b <- c(1,2,NA,NA,NA,6)
c <- as.Date(c("2021-01-01", "2021-01-02", NA,
           NA, NA, "2021-01-06"))
df <- data.frame("Group" = a, "Value" = b, "Date" = c)

take_max <- function(data, group, value, new_col_name, fun) {
  data %>% group_by() %>% 
    mutate( := if_else(
      all(is.na()),
      fun(NA),
      max(, na.rm = TRUE)
    ))
}

df %>% take_max(Group, Date, min_max, fun = as.Date)
df %>% take_max(Group, Value, min_max, fun = as.numeric)

It seems to work, but I get the following warning

Warnmeldungen:
1: Problem with `mutate()` input `new_col`.
i kein nicht-fehlendes Argument für max; gebe -Inf zurück
i Input `new_col` is `if_else(all(is.na(Value)), fun(NA), max(Value, na.rm = TRUE))`.
i The error occurred in group 2: Group = "B". 
2: In max(~Value, na.rm = TRUE) :
  kein nicht-fehlendes Argument für max; gebe -Inf zurück

My understanding of the problem is that in group B if_else tests if max(, na.rm = TRUE) (which in this case is equivalent to max(c())), would also be of the same type as fun(NA) and therefore evaluates both options. I tried to replace if_else with ifelse, but then the Date type is not preserved.

Would anyone have an idea of how to handle that?