Just check the user name to whom belongs your Nextcloud. Do e.g.:
ps -ef | grep -E "apache2|ngnix"
For me it is www-data
ps -ef | grep apache2
www-data 20722 20721 0 11:36 ? 00:00:17 /usr/sbin/apache2 -k start
www-data 20723 20721 0 11:36 ? 00:00:36 /usr/sbin/apache2 -k start
Now you can try to access to your external drive as this user, e.g. List files and create files:
sudo -u www-data ls -la /media/usb
and try to create file and see if you can:
sudo -u www-data touch /media/usb/testfile.txt
Basically you can refer to this: