It depends on how the system is configured, but it's pretty common to back up the contents of /etc, at least any configuration files in there that have been manually customized. It can get a little tricky to keep track of what stuff in /etc has been customized and what was the default configuration, though.
Sometimes, stuff under /var/lib can be backed up directly, but that often holds database files that really should be backed up using the database's own tools, as it's hard to get a clean snapshot by just copying the files with the database running. Specifically with Hestia, it's probably best to use its own backup tools (as Kairion linked to in the other thread), but that'd involve getting Hestia to start in the first place.
Speaking of which, the port numbers are different, but there's a section of the FAQ that looks like it describes a similar issue to what you were experiencing. You might at least compare the Nginx configuration in /etc with anything that shows up in /usr/local/hestia/install/deb/.
