Having different shapes of points for each line and making them shown on the legends

My goal is to make the graph look something like this My Goal. The problem I'm having is that ggplot won't let me use more than 6 kinds of shapes for the points, so my graph looks something like this right now current graph. How should I make it so that each line has it's unique shape of the points, but also making sure that they are shown cleanly and in the correct numeric order? (ie, not like this different shapes but unordered legend, and legend does not show the correct shapes of points, which is produced with the following code)

My data in data frame data_long:

structure(list(power1 = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
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3.80679536473264, 3.36223568778668, 3.26833864188926, 3.25649295550359, 
3.11084446590995, 2.86868707757046, 2.87914793117105, 2.7939746366475, 
2.57222595062283, 2.50336217394579, 2.08351142138273, 2.09604154052357, 
2.09111459705992)), row.names = c(NA, -506L), class = c("tbl_df", 
"tbl", "data.frame"))

density_vs_power <- ggplot(
  data = data_long,
  aes(power1, value, color = factor(group), group = group)
) +
  geom_line() +
  geom_point(shape = factor(data_long$group)) +
  scale_y_continuous(trans = "log10")

Also, is there a way to make the colors of the lines more discrete so that each adjacent line is more discernible?

Currently, the cleanest version looks like this best version, but it returns the warning: The shape palette can deal with a maximum of 6 discrete values because more than 6 becomes difficult to discriminate ℹ you have requested 23 values. Consider specifying shapes manually if you need that many have them.

Any help is much appreciated!

I would consider using some other aes / faceting / etc. to distinguish such a long list of parameters (grouping them somehow and using 6 shapes x 4 ltys or 4 colours x 3 shapes x 2 ltys for instance). Note the multiple comparison statistical limitations when interpreting such a plot.

However here is a solution that bruitforses ggplot to implement your idea:

data_long %>% 
  mutate(fgr = factor(group, levels = (as.integer(.$group)) %>% unique %>%  sort)) %>% 
  
ggplot(
  aes(power1, value, color = fgr, group = group)
) +
  geom_line() +
  geom_point(aes(shape = fgr)) + 
  scale_y_continuous(trans = "log10") +
  scale_color_discrete(name = "group")+
  scale_shape_manual(breaks = 1:23, values = 1:23, name = "group")