library(dplyr)

df %>% group_by(grp) %>% summarise(across(everything(), list(mean)))
#> # A tibble: 3 x 5
#>     grp     a     b     c     d
#>       
#> 1     1  3.08  2.98  2.98  2.91
#> 2     2  3.03  3.04  2.97  2.87
#> 3     3  2.85  2.95  2.95  3.06