Consider adding this wmic command:

wmic os get OSArchitecture

Code:

Microsoft Windows [Version 10.0.19042.867]
(c) 2020 Microsoft Corporation. All rights reserved.

C:\WINDOWS\system32>wmic os get OSArchitecture
OSArchitecture
64-bit


C:\WINDOWS\system32>

Run the following command on Command Prompt:

wmic os get OSArchitecture|Find "bit"

Code:

Microsoft Windows [Version 10.0.19042.746]
(c) 2020 Microsoft Corporation. All rights reserved.

C:\Windows\system32>wmic os get OSArchitecture|Find "bit"
64-bit

C:\Windows\system32>

Code:

@Echo off & Title Created By FreeBooter
Mode 80,18

Call :IsAdmin




For /F %%B In ('wmic Os Get /Format:List ^| Find /I "Osarchitecture"') Do (Set Output=%%B)
For /F "Tokens=*" %%C In ('Systeminfo ^| Find /I "OS Name"') Do (Set OsName=%%C)

echo. & echo. & Echo.

If  "%Output:~15,21%"=="64-bit"  (
    Echo         %OsName:~12,60% 64-bit
) else (
    Echo         %OsName:~12,60% 32-Bit
)

Pause >nul
Exit /B

:IsAdmin
>nul Reg query "HKU\S-1-5-19\Environment"  2>nul && ( goto :eof ) || (
    set params = "%*:"=""

    (     Echo Set UAC = CreateObject^("Shell.Application"^)
        Echo UAC.ShellExecute "cmd.exe", "/c ""%~s0"" %params%", "", "runas", 1 ) > "%temp%\getadmin.vbs"
    "%temp%\getadmin.vbs"
    exit
)
cls
goto :eof

A better version: no VBScript and administrative privileges are needed. The version number and build number are displayed.

Code:

@echo off&Title Created by Matthew Wai on TenForums.com&mode con cols=55 lines=6
(wmic cpu get AddressWidth /value|find "32")>nul&& set [#]=32-bit||set [#]=64-bit
echo.&echo.    You are running a %[#]% version of Windows.
For /f "tokens=2 delims==" %%# in (
'"wmic path Win32_OperatingSystem get Version /value"') Do (
echo     The version number is %%#)
For /f "tokens=2 delims==" %%# in (
'"wmic path Win32_OperatingSystem get BuildNumber /value"') Do (
echo     The build number is %%#)
For /F "Tokens=*" %%# In ('Systeminfo^|Find /I "OS Name"') Do (Set "[#]=%%#")
For /f "Tokens=2* delims=:" %%# in ("%[#]%") Do (Set "#=%%#")
Set "#=%#:                   =%"    
Echo     The product name is %#% & Pause>nul

Code:

@ECHO OFF
SETLOCAL

FOR /F "tokens=* USEBACKQ" %%F IN (`REG QUERY "HKLM\SOFTWARE\Microsoft\Windows NT\CurrentVersion" /v ProductName`) DO SET ProductName=%%F
SET ProductName=%ProductName:*REG_SZ =%
FOR /F "tokens=* Eol= " %%F IN ("%ProductName%") DO SET "ProductName=%%F"

IF DEFINED ProgramFiles(x86) (SET OSType=x64) ELSE (SET OSType=x86)

FOR /F "tokens=* USEBACKQ" %%F IN (`REG QUERY "HKLM\SOFTWARE\Microsoft\Windows NT\CurrentVersion" /v DisplayVersion`) DO SET DisplayVersion=%%F
SET DisplayVersion=%DisplayVersion:*REG_SZ =%
FOR /F "tokens=* Eol= " %%F IN ("%DisplayVersion%") DO SET "DisplayVersion=%%F"

SET UseExpresssion=Ver
FOR /F "tokens=*" %%F IN ('%UseExpresssion%') DO SET OSBuild=%%F
SET OSBuild=%OSBuild:*10.0.=%
SET OSBuild=%OSBuild:~0,-1%

ECHO %ProductName% %OSType% version %DisplayVersion% build %OSBuild%

ENDLOCAL
PAUSE

For a computer that cannot boot a bootable Windows 10 iso can be used to run commands in Windows Recovery Environment (RE).
An OP may not know about their computer and may borrow a flash drive iso.

There is a tutorial:
How to See Full Details about a Windows 10 ISO file or USB
steps 4 > 6 have commands for 32-bit and 64-bit architecture
See Full Details about a Windows 10 ISO file or USB

For How to Determine if Running 32-bit (x86) or 64-bit (x64) Architecture of Windows 10
the systeminfo command does not work in Windows RE.

In Windows RE, wmic commands can be used.