Combining two ggplots

I want to create a chart that shows the chronological progression of several events. These are two different types of events, firstly events that have only taken place on one day and secondly events that have taken place on several consecutive days, i.e. over a period of several days. So far I have created a ggplot for each of the two types of events. Since the number of events for the two types is not identical, I have already added an appropriate number of NA observations so that the ggplots can be combined. I have already tried to combine the ggplots with the operator +, but have not been successful so far.

library(ggplot2)
library(scales)
library(dplyr)
library(tibble)

df <- data.frame(c("2022-02-05", "2022-02-15", "2022-03-09", "2022-05-12", "2022-08-27"),
                   c("2022-02-05", "2022-03-08", "2022-03-09", "2022-05-12", "2022-08-28"),
                   c("event 1", "event 2", "event 3", "event 4", "event 5")
        )
colnames(df) <- c("start","end", "event")

df$start <- as.Date(df$start)
df$end <- as.Date(df$end)

# Split the data frame depending on whether the observations are a point in time or a time span
dftp <- filter(df,df$start == df$end)
dftp <- dftp %>%
  rename("date" = "start")
dfts <- filter(df,df$start != df$end)

# Add NA row such that both data frames have the same size
n <- nrow(dfts)
dfts[(n+1),] <- NA


# vary height and direction of the lines
dfts$position <- c(1,2,3)
positions <- c(0.5, -0.5, 1.0, -1.0)
directions <- c(1,-1)
line_pos <- data.frame(
  "date"=unique(dftp$date),
  "position"=rep(positions, length.out=length(unique(dftp$date))),
  "direction"=rep(directions, length.out=length(unique(dftp$date)))
)

dftp<- merge(x=dftp, y=line_pos, by="date", all = TRUE)
dftp <- dftp[with(dftp, order(date)), ]

text_offset <- 0.05
dftp$month <- as.numeric(format(dftp$date, "%m"))
dftp$month_count <- ave(dftp$date==dftp$date, dftp$date, FUN=cumsum)
dftp$text_position <- (dftp$month_count * text_offset * dftp$direction) + dftp$position

# change range of the plotted days
day_buffer <- 30
day_date_range <- dftp$date
day_format <- format(day_date_range, '%d %b')
day_df <- data.frame(day_date_range, day_format)




### 1. Plot (with time points)
timeline_plot<-ggplot(dftp,aes(x=date,y=0))
timeline_plot<-timeline_plot+theme_classic()

# Plot horizontal black line for timeline
timeline_plot<-timeline_plot+geom_hline(yintercept=0, 
                                        color = "black", linewidth=0.3)

# Plot vertical segment lines for events
timeline_plot<-timeline_plot+geom_segment(data=dftp[dftp$month_count == 1,], aes(y=position,yend=0,xend=date), color='black', linewidth=0.2)

# Plot scatter points at zero and date
timeline_plot<-timeline_plot+geom_point(aes(y=0), size=2)

# Don't show axes
timeline_plot<-timeline_plot+theme(axis.line.y=element_blank(),
                                   axis.text.y=element_blank(),
                                   axis.title.x=element_blank(),
                                   axis.title.y=element_blank(),
                                   axis.ticks.y=element_blank(),
                                   axis.text.x =element_blank(),
                                   axis.ticks.x =element_blank(),
                                   axis.line.x =element_blank(),
                                   legend.position = "bottom"
)

# Show day text
timeline_plot<-timeline_plot+geom_text(data=day_df, aes(x=day_date_range,y=-0.1,label=day_format),size=2.5,vjust=0.5, color='black', angle=90)

# Show text for each event
timeline_plot<-timeline_plot+geom_text(aes(y=text_position, label=event),size=2.5)


### 2. Plot (with time spnans)
timeline_plot2<-ggplot(data=dfts,aes(x=start,y=position))+geom_segment(aes(xend=end,yend=position),linewidth=1)

timeline_plot2<-timeline_plot2+geom_text(aes(label=event, hjust=1.1),size=2)


# Print plots
print(timeline_plot)
print(timeline_plot2)

My question now is how I can combine these two ggplots in such a way that I get a diagram in which all events are represented.