Login System In Batch
My main recommendation is that your variables have more descriptive names. While !x! may seem like a reasonable variable name for a counter that you're never going to use again, calling it something like !counter! makes your code easier for other people to maintain when there's a lot more of it.

I also got rid of ENABLEEXTENSIONS because that's enabled by default, and I moved cd users above :login_menu because if somebody enters an invalid user number and you're already in the users folder, your code will try to go into the users folder that's inside of the users folder and since there isn't one, you'll get an error.

To cut out that nested for loop, I stored the username map in an array. From there, you can determine whether or not a username is valid by if the variable exists.

Finally, I replaced the !s that you echoed with ^^!s so that they would be escaped. Because you have delayed expansion enabled, the last bit of your code would be displayed as HeyuserN because batch would consider ! You're logged in as ! to be a variable (because that's a valid variable name in batch).

If you could guarantee that you would never have more than ten users, you could build a string for a choice list to guarantee that the user would never enter an invalid user number, but I assumed this would be used by a large number of people.

@echo off
setlocal enabledelayedexpansion

cd users

:login_menu

set "user_counter=1"
for %%A in (*.user) do (
    echo !user_counter!. %%~nA
    set "users[!user_counter!]=%%~nA"
    set /a user_counter+=1
)
echo.

set /p "user_selection=Select user: "
if "%user_selection%"=="" goto login_menu
if not defined users[%user_selection%] (
    echo That user does not exist^^!
    pause
    goto login_menu
)
set "user_name=!users[%user_selection%]!"

:enter_password
for /f "tokens=1,2 delims=:" %%E in (!user_name!.user) do set "stored_password=%%F"
echo Enter your password, !user_name!
echo.
set /p "entered_password=Password: "

if "%entered_password%"=="%stored_password%" goto menu
echo.
echo That password is invalid^^!
pause
goto enter_password

:menu
echo Hey^^! You're logged in as !user_name!^^!
pause