This would work for your first plot:
library(dplyr)
library(tibble)
library(ggplot2)
library(tidyr)
df<- tribble(
~Value, ~Depth, ~Date,
-96.14, 10, 20211013,
-94.62, 20, 20211013,
-92.41, 30, 20211014,
-91.27, 40, 20211014,
-84.14, 50, 20211017,
-74.91, 60, 20211017,
-72.61, 70, 20211017,
-69.74, 80, 20211018,
-69.73, 90, 20211018,
-73.83, 100,20211019,
-77.27, 110,20211019,
-79.79, 120,20211019,
-80.89, 130,20211020,
-82.44, 140,20211020,
-82.43, 150,20211023,
-80.94, 160,20211023,
-80.11, 170,20211025,
-78.18, 180,20211025
)
# Transform Date so that it is an Actual Date class
df1 <- df %>%
mutate(
Date = as.character(Date) %>%
as.Date(format = '%Y%m%d')
)
# Plot one
df1 %>%
pivot_longer(
cols = Value:Depth,
names_to = 'measure'
) %>%
group_by(Date, measure) %>%
summarize(
value = mean(value)
) %>%
ungroup() %>%
ggplot(aes(x = Date, y = value, color = measure)) +
geom_point()

Regarding your second plot... could you explain more about what you want for the boxplots? A boxplot (such as the one drawn by ggplot2::geom_boxplot relies on computing quartiles, but your data doesn't have enough observations per date to do this computation. Is that just a product of your reprex, and your real dataset has more? Or are you just trying to get a sense of the data distribution for each date and for the "Depth" and "Value" measures?