Get stats of number of files of unqiue file extensions including binaries from command line

I am trying to recursively count the number of different extensions and how often each of them occurs in the files of a directory and I want to include the number of files with no extension. I am trying:

find . -type f -name "*.*" | grep -o -E "\.[^\.]+$" | 
  grep -o -E "[[:alpha:]]{2,16}" | awk '{print tolower($0)}' | 
   sort | uniq -c | sort -rn

But this does not display binaries with no extensions. How can I do this correctly?

UPDATE : My main intention is top find out how many files and its total size of terraform / terraform plugin binaries are downloaded in one particular folder so that I can view them and delete them.

The -name "*.*" in your find already excludes any file with no extension since you are looking only for files with at least one . and then, your grep is explicitly removing files without extensions:

grep -o -E "\.[^\.]+$" 

This will print the extension, but if the file has no extension it will print nothing:

$ echo 'foo.txt' | grep -o -E "\.[^\.]+$" 
.txt
$ echo 'foo' | grep -o -E "\.[^\.]+$" 
$

If what you want is to count the number of occurrences for each extension or no extension, try this instead:

find . -type f | 
    awk -F'.' '{
                 if(NF>2){ 
                    ext=tolower($NF)
                    k["."ext]++ } 
                 else{ k["no extension"]++ } 
               }
               END{ for(i in k){ print i":"k[i] } }'

For example, given this directory:

$ touch file{1..3}.txt file.jpg file.JPG file."weird extension with spaces" file
$ ls
 file   file1.txt   file2.txt   file3.txt   file.jpg  file.JPG 
 'file.weird extension with spaces'

You get:

$ find . -type f | 
>     awk -F'.' '{
>                  if(NF>2){ 
>                     ext=tolower($NF)
>                     k["."ext]++ } 
>                  else{ k["no extension"]++ } 
>                }
>                END{ for(i in k){ print i":"k[i] } }'
no extension:1
.txt:3
.weird extension with spaces:1
.jpg:2

Note that this will consider a hidden file, for example something named .hidden, as its own extension. That would be counted as one hit for the extension .hidden. Hidden files with extensions will be counted correctly (i.e. .hidden.txt will increase the hits for the .txt extension), but those without extension will not. I don't know how you want to handle that since extensions are largely cosmetic in Linux.

By the way, whether a file is binary or not has nothing to do with whether it has an extension or not.