I ended up using the Azure Functions Core Tools via PowerShell.

@echo off
echo Starting Azure Function deployment...

REM Navigate to function app directory
cd C:\my\path\

REM Clean and rebuild
call npm run clean
call npm run build

REM Set variables
set functionAppName=dev-funcapp
set resourceGroup=devrg

REM Deploy
echo Deploying to %functionAppName%...
call func azure functionapp publish %functionAppName% --verbose

echo Deployment completed!