Leaflet overlayGroups cause circle markers to not be clickable

Question

I'm working on a Leaflet map that will be part of a Shiny application. This map involves being able to click on a point to allow a plot to generate based on the input click. The map has an overlay group that can be toggled on and off. In this example, a simple popup displaying the name of the city will show up when the point is clicked.

Problem
When the map is initialized, the points are clickable. When the overlayGroup is turned off with the layersControl, the points are clickable. Once the overlayGroup is turned back on, the points are no longer clickable. This only affects the points that are covered by the overlayGroup (see the Myrtle Beach point).

What I've Tried
When there are multiple baseLayers that can be toggled by addLayersControl(), the circle markers are always clickable as the baseLayers are changed using this solution. This does not work with overlayGroups. I would like to find a similar solution with using overlayGroups that always keeps the circleMarkers on top so they are able to be clicked.

Code

# sample test of overlay groups in Leaflet

# load libraries
library(sf)
library(leaflet)

# get sample spatial data
demo(nc, ask = FALSE, echo = FALSE)
plot(nc)

# data frame for points
points <- data.frame(location = c("Greensboro","Charlotte","Raleigh","Myrtle Beach"),
                     lat = c(36.056,35.208,35.767,33.688),
                     long = c(-79.791,-80.847,-78.636,-78.908))

# Leaflet
leaflet(data = nc) %>% 
  addProviderTiles(providers$CartoDB.Positron) %>% 
  
  # Polygon layer
  addPolygons(data=nc, stroke = T, fillOpacity = 0, weight = 3, 
              color = "black", label = ~NAME,
              labelOptions = labelOptions(noHide = F, textsize = "12px", 
                                          style = list("font-weight" = "bold")), 
              group = "State") %>%

  # Point layer
  addCircleMarkers(data = points, lng = ~long, lat = ~lat, fillColor = "green",
                   weight = 3, fillOpacity = 0.5, radius = 10, stroke = TRUE,
                   popup = ~as.character(paste("<strong>City Name: </strong>", points$location,"<br/>")),
                   group = "Points") %>%
  
  
  # Layers control - polygon as an overlayGroup
  addLayersControl(overlayGroups = "State")