Here is one example taken from here which shows different results/error
library(dplyr)
library(rstatix)
data %>%
     summarise(across(where(is.numeric),
      ~  cur_data() %>%
       levene_test(reformulate("Treatment", response = cur_column())))) %>%
    unclass %>% 
     bind_rows(.id = 'flux')
# A tibble: 3 × 5
  flux    df1   df2 statistic     p
  <chr> <int> <int>     <dbl> <dbl>
1 flux1     1     8     0.410 0.540
2 flux2     1     8     2.85  0.130
3 flux3     1     8     1.11  0.323
data %>%
     summarise(across(where(is.numeric),
      ~  .data %>%
       levene_test(reformulate("Treatment", response = cur_column())))) %>%
     unclass %>% 
     bind_rows(.id = 'flux')
Error: Problem with summarise() input ..1.
ℹ ..1 = across(...).
✖ cannot coerce class ‘"rlang_data_pronoun"’ to a data.frame
Run rlang::last_error() to see where the error occurred.
data
data <- data.frame(site = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L), 
                                    .Label = c("S1 ", "S2 ", "S3 "), class = "factor"), 
                   plot = structure(c(1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L), 
                                    .Label = c(" Tree 1 ", " Tree 2 ", " Tree 3 "), class = "factor"), 
                   Treatment = structure(c(2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L), .Label = c("T1", "T2"), class = "factor"), 
                   flux1 = c(11.52188065, 8.43156699, 4.495312274, -1.866676811, 3.861102035, -0.814742373, 6.51039536, 4.767950345, 10.36544542, 1.065963875), 
                   flux2 = c(0.142259208, 0.04060245, 0.807631744, 0.060127596, -0.157762562, 0.062464942, 0.043147603, 0.495001652, 0.34363348, 0.134183704), 
                   flux3 = c(0.147506197, 1.131009714, 0.038860728, 0.0176834, 0.053191593, 0.047591306, 0.00573377, -0.034926075, 0.123379247, 0.018882469))