How I can Speed up code built using purrr- Why is Furrr slower than purrr

Question

I'd like to know if there is a way to speed up a code built with purrr package. I tried to convert it into furr and use the multisession option, but it is even slower than the sequential version.

# rm(list = ls())

setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
#> Error: RStudio not running
getwd()
#> [1] "C:/Users/Angela/AppData/Local/Temp/RtmpOqCRC2/reprex-44604912759f-full-husky"

#load required packages 
library(mc2d)
#> Loading required package: mvtnorm
#> 
#> Attaching package: 'mc2d'
#> The following objects are masked from 'package:base':
#> 
#>     pmax, pmin
library(gplots)
#> 
#> Attaching package: 'gplots'
#> The following object is masked from 'package:stats':
#> 
#>     lowess
library(RColorBrewer)
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(tidyverse)
library(furrr)
#> Loading required package: future
library(future)   #for parallel computation
#remotes::install_github("HenrikBengtsson/parallelly", ref="develop") #to use multisession
library(parallelly)
library(tictoc)

set.seed(99)
iters<-1000

df<-data.frame(id=c(1:30),cat=c(rep("a",12),rep("b",18)),month=c(1:6,1,6,4,1,5,2,3,2,5,4,6,3:6,4:6,1:5,5),n=rpois(30,5))

df$n[df$n == "0"] <- 3
se<-rbeta(iters,96,6)
epi.a<-rpert(iters,min=1.5, mode=2, max=3)
p=0.2
p2=epi.a*p

df<-as_tibble(df)
# this defined function ensures any `n` from `df` will be itered with 10000 s and a and generated 10000 results
plan(multisession)
tic()
iter_n <- function(n) future_map2_dbl(.x = se, .y = p2, ~ 1 - (1 - .x * .y) ^ n)
list_1 <- df %>% mutate(Result = future_map(n, ~iter_n(.x))) %>% unnest(Result)%>% group_split(month)
toc()
#> 2.22 sec elapsed
plan(sequential)


#the same without parallelization 

tic()
iter_n <- function(n) map2_dbl(.x = se, .y = p2, ~ 1 - (1 - .x * .y) ^ n)
list_1 <- df %>% mutate(Result = map(n, ~iter_n(.x))) %>% unnest(Result)%>% group_split(month)
toc()
#> 0.08 sec elapsed

^{Created on 2022-05-08 by the reprex package (v2.0.1)}

I have read about an issue of using furrr with R studio (https://github.com/DavisVaughan/furrr/issues/195), so I followed the advice and downloaded the parallely package, but it doesn't change anything. Furrr is still slower than purrr (which is actually odd)

If someone is wondering what system I am using I am working with a Windows system.

Do you have any suggestion on how to speed up a code using purr or fixing the problem of furrr? This is just an example, but I have a huge database to deal with. Any suggestion is appreciated.