python script to change multiple blender files

I’ve programmed in python in totally different contexts, and am confused as to whether it’s possible (and if so, how) to do the following with the Blender python API.
I’ve got a set of .blend files which all need exactly the same change done (move one vertex of a path to a different location). It would save a lot of time not to have to open each of the files and make the change. My intuition is that if there is an API I should be able to write a python script which
-loops over a list of file names
-opens the file (without opening the user interface)
-changes the relevant settings
-saves the files to a different filename (e.g. by appending a suffix).

All the information I seem to find online involves opening a file in the blender interface and then using a python console within the interface to make changes – that does not help me a lot because the tedious part is actually manually loading each individual file.
If the above is possible – then where do I find the relevant files to be able to import the python api into python (import bpy ? )?

Many thanks!

Thank you - sounds like exactly what I need.