I was able to able to make some progress on this by following guidance I found here.
I added a .code-workspace file and specified a path to my sub-folder. VS Code then noticed my nested Azure Functions app and offered to setup the .vscode folder within that sub-folder:
By opening that new workspace I am now able to run/debug the function app.
However, I am not yet able to just open the root directory (instead of the workspace) and run/debug. I tried adding the launch section in the .code-workspace file (as shown in the example from that article) but it would not accept entries for the launch/compounds/configurations property. Perhaps that failed since I only have one such sub-folder project right now?
I'll need to solve this last part in order to get to my goal of a monorepo approach where I have both the front-end and back-end projects in the same root folder.