I don't know about packages that export all that information at once, they might exist. But indeed, the boot object is complex and contains many information that can not be saved as a single data.frame. But it's possible to extract the parts that are of interest as data.frames and save them.
Here are the named data fields in the boot object, they can be accessed with $:
names(boot)
# [1] ".refClassDef" "compare" "seed" "QDIFstat"
# [5] "rng" ".->HLstat" ".->sample" "alpha"
# [9] "QXstat" ".->QYstat" ".->MFstat" ".->QDIFstat"
# [13] ".->nboot" ".->seed" "field" ".->compare"
# [17] "HLstat" "nboot" ".->QXstat" ".self"
# [21] ".->alpha" ".->rng" "QYstat" "sample"
# [25] "MFstat" "show"
The ones that are printed by default are:
# Mitigated Fraction
boot$MFstat
# observed median lower upper
# Equal Tailed 0.44 0.4464 0.1424 0.7056
# Highest Density 0.44 0.4464 0.1520 0.7120
# Hodges-Lehmann
boot$HLstat
# observed median lower upper
# Equal Tailed -0.07335 -0.07335 -0.17175 -0.015505
# Highest Density -0.07335 -0.07335 -0.16050 -0.009750
# Quartile Differences
boot$QDIFstat
# observed median lower upper
# Q25 -0.041500 -0.041500 -0.10340 -0.000905
# Q50 -0.112525 -0.111175 -0.28190 0.023200
# Q75 -0.168000 -0.168000 -0.38656 0.005300
# Quartiles of con
boot$QXstat
# observed median lower upper
# Q25 0.054000 0.054000 0.021005 0.11275
# Q50 0.139275 0.139275 0.061400 0.31000
# Q75 0.315000 0.315000 0.173000 0.45250
# Quartiles of vac
boot$QYstat
# observed median lower upper
# Q25 0.01250 0.01250 0.00095 0.026000
# Q50 0.02675 0.02675 0.01665 0.144575
# Q75 0.14700 0.14700 0.02810 0.219250
Here, since they all have the same number and names of columns, it is possible to assemble them in a single data.frame (but obviously that wouldn't work with unmatched columns). You also need to add a column to know what statistic each row describes (since once they're assembled it would be harder to know).
library(tidyverse)
bind_rows(
as_tibble(boot$MFstat) %>%
add_column(stat = "Mitigated Fraction"),
as_tibble(boot$HLstat) %>%
add_column(stat = "Hodges-Lehmann"),
as_tibble(boot$QDIFstat) %>%
add_column(stat = "Quartile Differences"),
as_tibble(boot$QXstat) %>%
add_column(stat = "Quartiles of X"),
as_tibble(boot$QYstat) %>%
add_column(stat = "Quartiles of Y"))
# A tibble: 13 x 5
# observed median lower upper stat
# <dbl> <dbl> <dbl> <dbl> <chr>
# 1 0.44 0.446 0.142 0.706 Mitigated Fraction
# 2 0.44 0.446 0.152 0.712 Mitigated Fraction
# 3 -0.0734 -0.0734 -0.172 -0.0155 Hodges-Lehmann
# 4 -0.0734 -0.0734 -0.161 -0.00975 Hodges-Lehmann
# 5 -0.0415 -0.0415 -0.103 -0.000905 Quartile Differences
# 6 -0.113 -0.111 -0.282 0.0232 Quartile Differences
# 7 -0.168 -0.168 -0.387 0.00530 Quartile Differences
# 8 0.054 0.054 0.0210 0.113 Quartiles of X
# 9 0.139 0.139 0.0614 0.31 Quartiles of X
# 10 0.315 0.315 0.173 0.452 Quartiles of X
# 11 0.0125 0.0125 0.00095 0.026 Quartiles of Y
# 12 0.0268 0.0268 0.0167 0.145 Quartiles of Y
# 13 0.147 0.147 0.0281 0.219 Quartiles of Y