Hi,
Here is my first attempt for drawing the circles on an image
library(ggplot2)
library(magick)
image <- image_fill(logo, 'none')
raster <- as.raster(image)
imgHeight = image_info(image)$height
imgWidth = image_info(image)$width
myData = data.frame(x = runif(10, 0, imgWidth),
y = runif(10, 0, imgHeight))
ggplot() +
annotation_raster(raster, 0, imgWidth, 0, imgHeight) +
xlim(0, imgWidth) + ylim(0, imgHeight) +
geom_point(data = myData, aes(x = x, y = y),
color = "orange", size = 10, shape = 1, stroke = 2)+
theme_void()

First I converted the image to a raster using the magick package. Then I used ggplot to create an empty plot with the dimensions of the figure, after which I plotted circles (geom_point) given certain coordinates.
This could easily be implemented in Shiny, but instead of ggplot a better implementation would be with plotly as you can use the proxy to only update the circles and not the whole image (will be slower). I didn't have time yet to figure out that part since I'm a plotly beginner myself 
Hope this already helps,
PJ