Check MySQL error log, e.g. /var/log/mysql/error.log

Check PHP error log, e.g. /var/log/php7.2-fpm.log

Also, check elgg-config/settings.php

For checking FQDN, run hostname and look at /etc/hosts

A few months ago our customer had same issue on the GoDaddy hosting. The problem was solved after renaming the Elgg root installed folder w/o any .dots in its name.

Ask your hosting provider about this.

I just want to thank you for all your comments and help, this issue has now been resolved!

After installing another CMS on the same server I got the following error: 
Important: HTTP Loopback Connections are not enabled on this server.

After a bit of Googling I added my ip and my.domainname.com record to my server /etc/hosts file and I am now able to use upgrade.php function without any errors. 

Thank you all and I'm sorry to have taken the elgg community time with something unrelated.