My search for the tools in Vivado and Quartus has come to an end. After three days of unsuccessful attempts to track down the processes while running Vivado and find the tools for each part of the design flow, I have given up and decided to resort to tcl commands which is well documented and also suggested on the yosys wiki page. The Vivado processes had dependencies such as libraries to be preloaded or variables of paths to be specified, which I was able to find looking at the shell scripts. However, even after specifying those dependencies error messages showed up saying the file was corrupt. Quartus had much better documentation of the command line tools which I can read about. Therefore, figuring out the tools for the design flow was not much of a problem.
After reporting my findings to my supervisor, I was told to come up with a suitable class structure to code. I was able to understand the existing structure of the code that was made by the previous intern, and figured that not much would have to be changed. However, I ran into an obstacle. The framework code was required to send a file at each of the design processes so that the user could make minor changes along the way. However, Vivado and Quartus did not seem to explicitly show those files. This would hopefully be my final challenge to work on next week finishing up the code.