"Parallels doesn't change the file associations. Parallels registers Windows apps (like Edge) for macOS in case users want to open them/files using macOS interface. macOS then decides what apps to use for this or that file type or protocol. Based on our testing if there is already a file association, then a new app registered in the system doesn't change it. Tip: Parallels provides an option to disable sharing Windows apps with macOS. It is enabled by default as the vast majority of customers like it. File associations can also be changed anytime using "Get Info" in file context menu and then "Open with:" and "Change All..."."
In other words, it looks like .html files were associated to your (in-Windows) Edge, hence it booting up a VM etc. but that can easily be mitigated.