control y-axis title positions when combining several plots with patchwork package

I would like to be able to control the y-axis title position for each plot with respect to the y-axis itself, so that when I input differing antibiotic name lengths into the top plot, the y-axis title in the bottom plot is the same distance from the y-axis and I do not have to manually change this in the bottom plot everytime I change the antiobiotic names in the top plot. Anyone able to help?

The first plot shows the default without any adjustment.

The second plot shows the desired distance the y-axis title should be from the y-axis labels.

The third plot demonstates how varying the antibiotic name length in top plot means the correction needs to be changed. I would like to try to code this to happen automatically.

library(tidyverse)
library(patchwork)

therapy_1 <- tibble(
  antibiotic = c("IV Piperacillin-tazobactam", "IV Piperacillin-tazobactam"),
  time_point = c("start", "end"),
  date = c("2023-04-10","2023-04-25")) %>% 
  mutate(date = as_date(date))

therapy_2 <-tibble(
  antibiotic = c("PO co-trimoxazole", "PO co-trimoxazole"),
  time_point = c("start", "end"),
  date = c("2023-04-10","2023-04-25")) %>% 
  mutate(date = as_date(date))

inflammatory_markers <- tibble(
  date = c("2023-04-10", "2023-04-12"),
  value = c("38.1", "37.8")) %>%
  mutate(date = as_date(date))

p1 <- therapy_1 %>%
  ggplot(aes(x = date)) +
  geom_line(aes(y = antibiotic, colour = antibiotic)) +
  theme(legend.position = "none")

p2 <- therapy_2 %>%
  ggplot(aes(x = date)) +
  geom_line(aes(y = antibiotic, colour = antibiotic)) +
  theme(legend.position = "none")

default <- inflammatory_markers %>%
  ggplot(aes(x = date)) +
  geom_point(aes(y = value))

desired <- inflammatory_markers %>%
  ggplot(aes(x = date)) +
  geom_point(aes(y = value)) +
  theme(axis.title.y = element_text(margin = margin(r = -160)))

# default output
p1 / default

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# desired output
p1 / desired

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# when length of y-axis labels shortened
p2 / desired

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^{Created on 2023-05-08 with reprex v2.0.2}

That's actually not exactly trivial (with patchwork). The solution which I am suggesting would also not be perfect. I think the easiest hack would be to use a custom annotation as your y axis title instead of a real y axis title. It is not perfect, because the size of the plots still vary and the annotation position will be located depending on your x scale.

## adding a custom annotation to your inferior panel. 
desired <-
  inflammatory_markers %>%
  ggplot(aes(x = date)) +
  geom_point(aes(y = value)) +
  ## annotate with geom_text and not annotate, because you are using dates
  ## and you want to use "nudge_x" which doesn't work with annotate
  geom_text(
    data = data.frame(), aes(
      label = "value",
      x = min(inflammatory_markers$date),
      y = 1.5
    ),
    angle = 90, nudge_x = -.4
  ) +
  ## limit coordinates and turn clipping off
  coord_cartesian(xlim = range(inflammatory_markers$date), clip = "off") +
  ## remove y label
  labs(y = NULL)

# default output
p1 / desired

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p2 / desired

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^{Created on 2023-05-08 with reprex v2.0.2}

Different enough to merit a second answer (IMO). If you're happy to use another package, you can also use egg::ggarrange which should do exactly what you need.

library(egg)

ggarrange(p1, desired)

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ggarrange(p2, desired)

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^{Created on 2023-05-08 with reprex v2.0.2}