Various suggestions and solutions from users/programmers all point to a likely folder corruption due to the sudden PC reboot. However, I've never been entirely convinced by two things:
1: Because the classes weren't recognized when building a project in another directory.
2: because of the following error:
Error while loading [...]: Exception thrown: System.TimeoutException: The operation has timed out.
And it was precisely this last error that prompted me to investigate further within VS Code. In fact, the compiler was trying to establish a connection with the "LSP" (I assume the acronym for Language Service Protocol), but was unsuccessful.
Searching for "Omnisharp" in the VS Code settings search engine, I came across the following option:
Which was disabled (perhaps because of the sudden PC reboot?). By enabling it, VS Code finally recognized the Unity classes.
VS Code now recognizes classes
I hope this helps other users, please make changes with caution!