Terminal PATH startup message
Method #1, inspection of files

Depending on how the software installed it likely would've one or more of these files:


/etc/profile
/etc/bashrc
~/.bash_profile


Given it's a Linux scripted installer running on macOS it will likely have created some additional files which are typically not present on macOS but can augment the behavior of Bash when they're encountered.


~/.bashrc
/etc/profile.d/*


I'd take care to go through all these locations' files and inspect them for any residual cruft from the Linux installer.

Method #2, searching

Since you have some hints from that $PATH output you could search for files that contain bits from that string. For example:

$ grep -r '/Applications/Xamarin Workbooks.app' /etc ~


And then make note of any files that are returned. These would be the files that require repair.