using System;
using System.IO;
using System.Linq;
using System.Text.Json;

//get the list of file paths
var files = Directory.GetFiles(@"C:\tmp");

//group by extension and get file names
//first method
var query1 = files.GroupBy(
    Path.GetExtension,
    Path.GetFileName);

//second method
var query2 = files.GroupBy(
    file => Path.GetExtension(file),
    file => Path.GetFileName(file));

//third method
var query3 =
from file in files
group Path.GetFileName(file)
by Path.GetExtension(file);

Console.WriteLine(JsonSerializer.Serialize(query1));
Console.WriteLine(JsonSerializer.Serialize(query2));

//output to console
foreach (var group in query3)
{
    Console.WriteLine("Extension: " +
        group.Key);
    foreach (var file in group)
    {
        Console.WriteLine("  - " + file);
    }
}

//output is:
//Extension: .xml
//  - data.xml
//  - file.xml
//Extension: .txt
//  - samples.txt