ggplot2 - Incorporating scale_fill_manual with ggalt to create custom colour palette for dumbbell plot

I am working on building a plot to map intervals of time for several items of interest.

To do this, I have built a dumbbell plot with ggalt. I am trying to unify my colour schemes across multiple graphs to ensure the same time periods are the same colours across graphs. In particular, I am creating other graphics where "Interval 1" is important and highlighted elsewhere; having uniform colour schemes will help interpretation.

Can geom_dumbbell recognize my custom palette as I would for other plots usually? I would like to have the custom palette to be modifiable globally rather than being defined at each graph.

The only similar question that I can find is this one which unfortunately just overlays a geom_point to produce a legend... This might work but seems quite clunky.

library(ggplot2)
library(ggalt)

df <- tibble(x = c(4,6,5,8,10), y = c(8,9,10,12,15), z = c(14,12,14,15,18), d = c("A","B","C","D","E"))

legend_colors<- c("Interval 1" = viridis(1, option = "C", begin = 0, end = 0.1), 
                  "Interval 2" = viridis(1, option = "C", begin = 0.1, end = 0.2),
                  "Interval 3" = viridis(1, option = "C", begin = 0.5, end = 0.7))

df %>%
  ggplot() +
  geom_dumbbell(aes(x = x, 
                xend = y, 
                y = d), 
                colour = "Interval 1",
                colour_xend = "Interval 2",
                size = 2) +
  geom_dumbbell(aes(x = y,
                    xend = z, 
                    y = d),
                colour = "Interval 2",
                colour_xend = "Interval 3",
                size = 2) +
                scale_colour_manual(values = legend_colors) +
                theme_clean()

I want to produce a graphic like this but with colours that are defineable outside of the graph code itself. Sample Graphic

One option to achieve your desired result would be to reshape your data to long and use a geom_point + geom_line:

library(ggplot2)
library(viridis)
library(ggthemes)
library(tidyr)

names(legend_colors) <- c("x", "y", "z")

df |>
  pivot_longer(-d) |>
  ggplot(aes(value, d)) +
  geom_line(aes(group = d, color = name), size = 1) +
  geom_point(aes(color = name), size = 2) +
  scale_color_manual(
    values = legend_colors
  ) +
  theme_clean()