What does HR mean by “We will be in touch within the next few weeks to provide feedback and confirm next steps”? Is there any deeper meaning to it?

In the nutshell, No, there is no inner meaning. In fact, in my experience this message is void of any meaning at all.

First off, if you are not selected to continue in the interview process, chances are good you will never hear from this employer again. They gain little by making the effort to contact you just to inform you that you are no longer a candidate.

Second, two weeks is a suspicious time interval. One thing you can take to the bank; if they aren’t in touch in two weeks, you are no longer a candidate. Don’t be fooled by the soft language. HR’s statement is equivalent to the less-encouraging early-twentieth-century response, “Don’t call us. We’ll call you.”

Most employers will not provide useful feedback even under torture. If you are selected to continue, that will be your feedback. If you are not selected, they will say little or nothing, because virtually anything they say may become part of a lawsuit if you are the litigious type. If you do get feedback, thank them sincerely for treating you like a human being. They are taking a risk for something that is of no benefit to them.