Your analysis seems correct. If she didn't ask you any questions or imply the desire for more information, I think you can and should leave it at that, for now. Once a "sufficient" back and forth chain of thank you notes has occurred there is no reason to extend it.
However, if the need arises in future to communicate with her you can open with thanks for past help and encouragement. You could also, then, let her know of any success generated by yer suggestions.
As you note, some emails are just noise. Some are nice, but not essential. Some are essential. This sounds like it would be just noise and she is likely busy encouraging the next person.
However, if you do take her suggestions and things work out well for you as a consequence, you can then write with the appropriate thanks and update.
I seldom reply to emails such as the one you describe unless I have something to say that will benefit the receiver in some way. There are exceptions, of course.