What definition of Gain of Function do you think is correct?
That's a fair question, and worth serious discussion.
Let's stick with using NIH's definition here, in the the context of this dispute between Senator Paul and Dr. Fauci.
In 2016, the NIH defines the term as "Gain-of-function (GOF) research involves experimentation that aims or is expected to (and/or, perhaps, actually does) increase the transmissibility and/or virulence of pathogens."
The discussion you link to from the 2014 symposium doesn't contradict that, noting "any selection process involving an alteration of genotypes and their resulting phenotypes is considered a type of Gain-of-Function (GoF) research", but then goes on to clarify that there is a lack of clarity regarding the then-current US policy, which the organizers and participants were keen to note applied only to "dangerous" or problematic research dealing with organisms likely to harm human health "even if the U.S. policy is intended to apply to only a small subset of such work."
Those two sources, the 2015 summary of the 2014 symposium Potential Risks and Benefits of Gain-of-Function Research and the Gain-of-Function Research: Ethical Analysis paper also linked above were, and are, top Nexis and Google search results and provide the best context for the definition of the term as understood by the two men.
The dispute, which Fauci certainly was intimately familiar with was not about the definition of the term "Gain of Function", but about which types of Gain of Function research were either too dangerous to pursue, or which should be prohibited from recieving US funding. That's an important distinction.
The most generous interpretation of Fauci's answers to Senator Paul's questions is that he wasn't denying that the NIH had ever funded anything that met the strict definition of GOF as "any selection process involving alteration of genotypes...", because he knew for a fact that the NIH certainly was funding research that met that definition. He had to be answering a question that Paul didn't ask, something along the lines of "Did you ever fund the types of GOF research that had been prohibited by the United States". But even that more generous reading of Fauci's remarks doesn't save him. There's at least reasonable suspicion that the NIH did, in fact, provide funding, if only indirectly, for GOF research on respiratory viruses; exactly the type of research that was identified even at the 2014 "Potential Risks" symposium.
As an aside, Ralph Baric himself provides a particularly lucid description of exactly which types of GOF research were dangerous, but worth the risk, too dangerous, or not at all dangerous, at least in his mind. It's long, so I won't quote it, but it's easy to find at the link you provided.
It's not necessary to impute evil intent to Fauci, and Baric, Daszak, and all the rest, only arrogance. Fauci has a long history of employing the "Noble Lie", beginning at least with the AIDS epidemic, and his knowingly false claims that the HIV virus was a universal threat, spreadable by casual contact. He's discussed his reasons for that, and it's not particularly germain here except as a marker of the man's general proclivity to lie to the public when it suits what is, in his mind, a sufficiently noble purpose.
Finally, Paul's op-ed in Newsweek of all places does a perfectly good job of laying out the senator's case against Dr. Fauci in this matter. It won't get him convicted in a court of law, but that really isn't Paul's aim. He's wants to show exactly how the public health authorities exceeded their authority, lied to and mislead the public and their elected representaitives, and contributed to the badly bungled the response to what certainly could have been a disasterous pandemic.
“Let’s stick with using NIH’s definition here,”
That would be fine if what you were doing is citing “the NIH’s definition”.
In fact what you linked to is a definition written by a bioethics professor who is the director of the “Centre for Human Bioethics” in Australia.
He doesn’t work for the NIH nor is his opinion “the NIH’s definition”. And his doctorate is in Philosophy, not medical research..
The 2015 symposium that I had linked to was organized by researchers sponsored by National Research Council and the National Academy of Science,
And as can be seen in their discussion, “Gain of Function” is a term that they invented circa 2012 and which didn’t have a fixed meaning when the Obama administration sought to ban high risk experimentation that could be covered under that umbrella term. Their objection is that GoF isn’t well defined and it also includes research that isn’t risky.