Why doesn't this data.table function modify the argument?

I'm trying to get learn the data.table package, which seems fantastic.

One behaviour I'm unable to google my way to understanding is the following: I want to use a function to create a variable by reference. If the data input is a data.frame I also want to make it a data.table, and this works - but the variable defined is only created if the data input is already a data.table. This seems strange to me, anyone knows the reason for this?

E.g. after running the bar function (which makes the input a data.table if it isn't already, and then defines a variable bar) on the data.frame X, X will be a data.table but the variable bar is not created. However, on Y (X coerced to a data.table), the variable bar is created. Why isn't the variable bar created in X?

library(data.table)
bar <- function(x){
    if(!"data.table" %in% class(x)) setDT(x)
    x[, bar := 1:.N]
    invisible(NULL)
}
X <- data.frame(foo = letters[1:2])
Y <- as.data.table(X)
str(X)
## 'data.frame':    2 obs. of  1 variable:
##  $ foo: chr  "a" "b"
bar(X)
str(X)
## Classes 'data.table' and 'data.frame':   2 obs. of  1 variable:
##  $ foo: chr  "a" "b"
str(Y)
## Classes 'data.table' and 'data.frame':   2 obs. of  1 variable:
##  $ foo: chr  "a" "b"
##  - attr(*, ".internal.selfref")=<externalptr> 
bar(Y)
str(Y)
## Classes 'data.table' and 'data.frame':   2 obs. of  2 variables:
##  $ foo: chr  "a" "b"
##  $ bar: int  1 2
##  - attr(*, ".internal.selfref")=<externalptr> 

I'm using R 4.2.0 and data.table 1.14.2

UPDATE: this is essentially the same question as in

Using setDT inside a function

and the answer provided there clarifies the issue. Thanks to Waldi for pointing me to this.