I am trying to generate ridge plot like the one described

I think this is harder to interpret, less honest, and arguably less attractive than a simple line plot.

toplot %>%
  ggplot(aes(factor(Year), n, color = genes, group = genes))  
  geom_line(size = 1.5)  
  geom_point(size = 4, shape = 21, fill = "white")  
  scale_color_manual(values = c("deepskyblue4", "orange"))  
  labs(x = "Year")  
  theme_light(base_size = 16)

^{Created on 2022-04-24 by the reprex package (v2.0.1)}