No worries. 
Mint is based on Ubuntu, which itself is based on Debian. So your packages are primarily in deb format, optionally followed by Flatpak. For the former, it’s managed via the apt command, and for the latter, it’s flatpak.
According to the directory listing, your nomad user profile doesn’t have an existing Syncthing configuration under /home/nomad/.config.
Depending on which version of Syncthing you’ve got and when you first started using it, your Syncthing config might be following the XDG directory tree layout. So check for the existence of a .local/state/syncthing directory and .local/state/syncthing/config.xml file.
(See Syncthing’s documentation for more details: https://docs.syncthing.net/users/config.html)
So in your original post when you said “I have forgotten my password for the syncthing GUI so i editted the config file to remove the user name and password.”, do you recall where the config file is/was?
On Linux systems, package managers won’t touch users’ configuration files, but will remove system-wide configuration files only if they haven’t been locally changed (i.e. still match the originals from the package).
On Unix/Linux, binary executables generally don’t have filename extensions. There are some exceptions such as .AppImage, but even that’s just for user convenience. A binary executable can be named anything a user wants.
Scripts also don’t require a filename extension, although traditionally it’s .sh for dash, Bash and other Bourne shell like scripts, .pl for Perl, .php for PHP, .py for Python, .go for Go and so on.
In Unix/Linux, it’s all about the magic number – a sequence of bytes at the beginning of a file that can (generally) uniquely identify the file type: List of file signatures
Manually downloading and installing software is an option, but it’s much more common to use a package manager in Linux.
Because Syncthing comes packaged as a single file, you might have downloaded it and run it directly from /home/nomad/Downloads, or it’s on your desktop, or /usr/local/bin, or /opt, or somewhere else.
But since you have /usr/bin/syncthing and it’s owned by root:root, it’s more than likely that it came from a .deb package either from the Linux Mint or Syncthing repositories.
If you have a /etc/apt/sources.list.d/syncthing.list file, then it’s almost guaranteed that you’re using Syncthing’s official repo: https://apt.syncthing.net/
Most desktop Linux systems are set up with day-to-day user activities done from a non-root user account to enhance security (e.g. makes it much harder for a rootkit and/or other malware to take a foothold).
Not that you should, but if you really, really want to nuke /usr/bin/syncthing…
sudo rm /usr/bin/syncthing
… or change the ownership to your “nomad” login…
sudo chown nomad: /usr/bin/syncthing
… or update the timestamp to the current time:
sudo touch /usr/bin/syncthing
(For more info about the sudo command: https://en.wikipedia.org/wiki/Sudo)
But the proper way to uninstall Syncthing is:
sudo apt remove syncthing
Or alternatively:
sudo apt purge syncthing
“purge” removes any system configuration files even if they’ve been locally modified (but still doesn’t touch user configuration files).
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