How to filter rows in both parent and nested tables, using reactable?

How to filter rows with a specific Type, which are either in the parent or in any of the nested tables of a reactable, using crosstalk::filter_checkbox, as shown here ?

dat <- structure(list(Manufacturer = c(
  "Acura", "Acura", "Audi", "Audi",
  "BMW", "Buick", "Buick", "Buick", "Buick", "Cadillac", "Cadillac",
  "Chevrolet", "Chevrolet", "Chevrolet", "Chevrolet", "Chevrolet",
  "Chevrolet", "Chevrolet", "Chevrolet", "Chrysler", "Chrysler",
  "Chrysler", "Dodge", "Dodge", "Dodge", "Dodge", "Dodge", "Dodge",
  "Eagle", "Eagle", "Ford", "Ford", "Ford", "Ford", "Ford", "Ford",
  "Ford", "Ford", "Geo", "Geo", "Honda", "Honda", "Honda", "Hyundai",
  "Hyundai", "Hyundai", "Hyundai", "Infiniti", "Lexus", "Lexus",
  "Lincoln", "Lincoln", "Mazda", "Mazda", "Mazda", "Mazda", "Mazda",
  "Mercedes-Benz", "Mercedes-Benz", "Mercury", "Mercury", "Mitsubishi",
  "Mitsubishi", "Nissan", "Nissan", "Nissan", "Nissan", "Oldsmobile",
  "Oldsmobile", "Oldsmobile", "Oldsmobile", "Plymouth", "Pontiac",
  "Pontiac", "Pontiac", "Pontiac", "Pontiac", "Saab", "Saturn",
  "Subaru", "Subaru", "Subaru", "Suzuki", "Toyota", "Toyota", "Toyota",
  "Toyota", "Volkswagen", "Volkswagen", "Volkswagen", "Volkswagen",
  "Volvo", "Volvo"
), Model = structure(c(
  49L, 56L, 9L, 1L, 6L,
  24L, 54L, 74L, 73L, 35L, 79L, 22L, 30L, 17L, 58L, 59L, 15L, 20L,
  31L, 27L, 52L, 48L, 26L, 80L, 83L, 21L, 37L, 84L, 86L, 93L, 44L,
  41L, 90L, 64L, 68L, 13L, 89L, 33L, 62L, 85L, 66L, 25L, 11L, 43L,
  40L, 77L, 82L, 70L, 38L, 75L, 28L, 92L, 5L, 69L, 7L, 60L, 72L,
  2L, 4L, 19L, 32L, 63L, 36L, 78L, 14L, 71L, 61L, 12L, 34L, 81L,
  39L, 51L, 53L, 87L, 45L, 47L, 16L, 10L, 76L, 50L, 57L, 55L, 88L,
  91L, 23L, 18L, 67L, 46L, 42L, 65L, 29L, 3L, 8L
), .Label = c(
  "100",
  "190E", "240", "300E", "323", "535i", "626", "850", "90", "900",
  "Accord", "Achieva", "Aerostar", "Altima", "Astro", "Bonneville",
  "Camaro", "Camry", "Capri", "Caprice", "Caravan", "Cavalier",
  "Celica", "Century", "Civic", "Colt", "Concorde", "Continental",
  "Corrado", "Corsica", "Corvette", "Cougar", "Crown_Victoria",
  "Cutlass_Ciera", "DeVille", "Diamante", "Dynasty", "ES300", "Eighty-Eight",
  "Elantra", "Escort", "Eurovan", "Excel", "Festiva", "Firebird",
  "Fox", "Grand_Prix", "Imperial", "Integra", "Justy", "Laser",
  "LeBaron", "LeMans", "LeSabre", "Legacy", "Legend", "Loyale",
  "Lumina", "Lumina_APV", "MPV", "Maxima", "Metro", "Mirage", "Mustang",
  "Passat", "Prelude", "Previa", "Probe", "Protege", "Q45", "Quest",
  "RX-7", "Riviera", "Roadmaster", "SC300", "SL", "Scoupe", "Sentra",
  "Seville", "Shadow", "Silhouette", "Sonata", "Spirit", "Stealth",
  "Storm", "Summit", "Sunbird", "Swift", "Taurus", "Tempo", "Tercel",
  "Town_Car", "Vision"
), class = "factor"), Type = c(
  "Small", "Midsize",
  "Compact", "Midsize", "Midsize", "Midsize", "Large", "Large",
  "Midsize", "Large", "Midsize", "Compact", "Compact", "Sporty",
  "Midsize", "Van", "Van", "Large", "Sporty", "Large", "Compact",
  "Large", "Small", "Small", "Compact", "Van", "Midsize", "Sporty",
  "Small", "Large", "Small", "Small", "Compact", "Sporty", "Sporty",
  "Van", "Midsize", "Large", "Small", "Sporty", "Sporty", "Small",
  "Compact", "Small", "Small", "Sporty", "Midsize", "Midsize",
  "Midsize", "Midsize", "Midsize", "Large", "Small", "Small", "Compact",
  "Van", "Sporty", "Compact", "Midsize", "Sporty", "Midsize", "Small",
  "Midsize", "Small", "Compact", "Van", "Midsize", "Compact", "Midsize",
  "Van", "Large", "Sporty", "Small", "Compact", "Sporty", "Midsize",
  "Large", "Compact", "Small", "Small", "Small", "Compact", "Small",
  "Small", "Sporty", "Midsize", "Van", "Small", "Van", "Compact",
  "Sporty", "Compact", "Midsize"
), subtask = c(
  0, 1, 0, 1, 0, 0,
  1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1,
  1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0,
  0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1,
  1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1,
  1, 0, 1
)), row.names = c(NA, 93L), class = "data.frame")

library(tidyverse)
library(reactable)
library(crosstalk)

dat_task <- dat %>% filter(subtask==0)
tasks_with_subtasks <- dat %>% filter(subtask==1) %>% 
  pull(Manufacturer) %>% unique() 


reactable(dat_task[,1:3], details = function(index) {
  if(dat_task$Manufacturer[index] %in% tasks_with_subtasks){
    dat_subtask <- dat[dat$Manufacturer == dat_task$Manufacturer[index] & dat$subtask==1,1:3]
    htmltools::div(style = "padding: 16px",
                   reactable(dat_subtask, outlined = TRUE)
    )
  }
})