When across() is applied to 0 variable, it behaves differently depending on whether the tibble contains columns or not:

library(dplyr)
tibble(hello = 1:5) %>% mutate(across(NULL, ~ .x + 1))
# # A tibble: 5 x 1
#   hello
#   <int>
# 1     1
# 2     2
# 3     3
# 4     4
# 5     5
tibble(.rows = 5) %>% mutate(across(NULL, ~ .x + 1))
# Erreur : Problem with `mutate()` input `..1`.
# x Can't select within an unnamed vector.
# i Input `..1` is `across(NULL, ~.x + 1)`.
# Run `rlang::last_error()` to see where the error occurred.

This problem doesn't occur when using scoped verbs:

library(dplyr)
tibble(hello = 1:5) %>% mutate_at(NULL, ~ .x + 1)
# # A tibble: 5 x 1
#   hello
#   <int>
# 1     1
# 2     2
# 3     3
# 4     4
# 5     5
tibble(.rows = 5) %>% mutate_at(NULL, ~ .x + 1)
# # A tibble: 5 x 0

(Version of dplyr: 1.0.2)