Data quality - check if all values in a character column are numbers in R

I am looking to perform data quality on numerous system generated tables. One of the checks is to see if all values in a character column are only numbers. I am looking to know the number columns where this check is true. Using the following table as an example I would want to identify that two columns (code and age) are character columns that consist of only numeric values.

Table Structure

Column Name	Data Type
name	character
type	character
code	character
member_id	integer
collection_date	date
age	character
height	double

Table Values

Column Name	Column Values
name	only letters
type	only letters
code	only numbers
member_id	only numbers
collection_date	only dates
age	only numbers
height	only numbers

I am having issues thinking of the logic that is required to do this. What I have done thus far is:

To select only columns that are character data types

df %>%
  dplyr::select_if(is.character)

To validate that all values in the column are numeric (or null, which is fine)

sum(varhandle::check.numeric(df$code)) == nrow(df)

I am hoping to build a function that performs this across all columns and stores the number where the check is true into a column (i.e. dplyr::mutate), but I am not sure how to structure this; is it an across, an apply, or something else. Or is there any existing function/package that would perform this task? Any help is appreciated.

Solution

We could construct the condition within select itself

library(dplyr)
iris %>%
   select(where(~ all(varhandle::check.numeric(.))))

It is not clear whether numeric columns with mismatched type or columns having some character elements and thus got converted to class character. If it is the former, then add a type.convert before the select and then get only the numeric columns

df %>%
   type.convert(as.is = TRUE) %>%
   select(where(is.numeric))