composer dump-autoload will make the existing classes available. But does the Class 'Monolog\Handler\StreamHandler' exist? You could check that in the vendor directory.
Now what is the effect of the minimum-stability property? It affects dependency resolution, that means how composer determines which package versions to install. I guess in this case it's about a difference between versions of the Monolog package. The class is expected in it but the installed version somehow does not include it.
That's my guess where I'd look for the cause of the error.
If you want to try to set minimum-stability and your composer.json does not have it, you could add it.
If it doesn't help, could you please look into composer.lock and see which version of Monolog is installed?