Change value in group according to first occurrence

I have this type of dataframe

    df <- data.frame(
        Hospital_ID= c(1,1,1,2,2,2,3,3,3),
        COVID = c("YES", "NO", "", "NO", "", "NO", "NO", "NO", "YES"))
    
      Hospital_ID COVID
1           1     YES
2           1     NO
3           1      
4           2     NO
5           2      
6           2     NO
7           3     NO
8           3     NO
9           3     YES

Column COVID is YES if there is some pactient with COVID and NO if there not and empty space if there was no tested patient

And I would like to change in another column value of COVID in group like this

      Hospital_ID COVID  COVID_IN_HOSPITAL
1           1     YES    YES
2           1     NO     YES
3           1            YES
4           2     NO     NO
5           2            NO
6           2     NO     NO
7           3     NO     YES
8           3     NO     YES
9           3     YES    YES

I try this code

df%>% group_by(Hospital_ID)%>% mutate(COVID_IN_HOSPITAL = ifelse(COVID = "YES", "YES", "NO")%>%ungroup

But it was wrong