This is an opinion request this one because either approach works and based on this information plus the fact you seem keen on individual files. I would encourage just that.
Modular approach works with themes if you plan to provide the same functionality per theme as you won't need to edit functions per theme. I would go with individual files and just put them in a folder. If one of those files has a bug you'll be quick on applying the changes to all the themes you create.
If you put all the functions in one file and each theme gets its own versions of those files due to requests etc. Then you create a little more work in that you copy and paste code. Not a lot of work but then that demands on just how much that single file changes over the years or even within some months.
There is nothing wrong with many folders and files. It won't have an effect on loading. It would take hundreds of include() or require() before it becomes an issue.