Is there a way to add silence between phrases?

I'm afraid not. Not only can you not do this in Diagnostics, where you'd think it might be an option, but you can't set it up as a favorite either - you can create a favorite that will insert as many seconds as you want, but there's no way that you can execute it at a cursor point - it either has to be at the start or the end of your file, or at some proportionate percentage through it, which means that it inserts it at a different spot each time you change the file - pretty much useless.

Just the option to insert a favorite at the current cursor point would make so much difference - but no...

The easiest way to achieve some automation of this process is to use Generate>Tones, which remembers your last setting, and assign a keystroke to it. If you set all the sliders to zero, it will create silence for whatever time you had it previously set to, and it will place that much silence at the cursor point.