Extract into a dataframe the number of points in each buffer, in a set of concentric equi-distance buffers around a single point

I have the locations of the patients using an healthcare facility, and wants to extract the number of patients living at given distances from the hospital.
I generated buffers at 500m increments around the hospital, but not able to extract the number of patients in each buffer.
I was able to generate and plot the desired buffers, was also able to intersect with the patient locations, but was not able to get out the desired output.

suppressMessages(library(sf))
suppressMessages(library(tmap))
suppressMessages(library(maptools))
suppressMessages(library(rgeos))
suppressMessages(library(dplyr))

setwd("C:/SpatTemp/gwr_lg_data")
Lagos <- readShapePoly("Lagos_State_LGAs")
Lagos<- st_as_sf(Lagos, coords = c("Longitude", "Latitude"),
                 crs = "+proj=longlat +datum=WGS84")

setwd("C:/SpatTemp")
pract<- read.csv("First.csv")
pract_sf <- st_as_sf(pract, 
                     coords = c("Longitude", "Latitude"),
                     crs = "+proj=longlat +datum=WGS84")

hospt<-read.csv("Hospital.csv")
hospt_sf<- st_as_sf(hospt, 
                    coords = c("Longitude", "Latitude"),
                    crs = "+proj=longlat +datum=WGS84")

hospt_BNG<- st_transform(hospt_sf, 27700)
rad<- seq(25000,500, by=-500)

for (x in rad) {               
 plot(st_geometry(st_transform(st_buffer(hospt_BNG, x), 4326)))
              }
 
for (x in rad)  { 
        pract_sf %>% st_join(st_transform(st_buffer(hospt_BNG, x), 4326), ., left = FALSE) %>% 
              count(Address)
          }