With respect to timing, there was no pandemic in January, we're not going to see 'public fear and pandemonium' until it hits home, which wasn't until March. It wasn't until this point could there have been a true run on anything at least in the US.
The delineation between HCW PPE and 'civilian' PPE is basically moot: both N95 and surgical masks are widely used by civilians and HC.
Given the above, if there were any real impetus by 'the nations top doctor' to buy masks there would have been a massive run on all kinds of masks.
The reason that 'you are able to buy something' is precisely because the policy was 'masks are not important'.
Understand that in 2020 (and arguably today), nobody knew the difference between the various kinds of masks. 'N95' was not in the public lexicon. Masks are Masks. If the 1/2 of Americans that seem to be concerned about COVID felt that they needed masks, they would have bought them.
It would be impossible for Dr. Fauci or anyone else to say: "Buy this kind of mask over here, but that other kind of mask, don't worry about that, you don't need it" - this is beyond the threshold of complexity of something you can effectively message to 350 Million people.
The amount of pricing pressure etc. would have made it clearly more difficult for HCW around the world to get access to much of the gear they needed - we know this because even without face masks doctrine, there were a lot of shortages.
Doctors in many facilities were resigned to having to re-use a lot of gear - including masks.
If there were a public stampede for those masks, they would have had critical shortages that would have materially affected outcomes.
It wasn't until summer 2020, when COVID numbers started to come under control, that 'resource sharing' started to become effective, and that supply chains truly started to be able to handle demand did things start to seem more reasonable.
Only in June/July did a lot of HC centres across the nation start to receive major shipments of PPE.
At that point 'we made it through Phase 1' - at which time, it started to make sense to make masks part of the public health strategy.
So then the communication shifts: they start telling us how great masks are, how they can help us, and that we should wear them.
Obviously, this feels disingenuous, but it's not.
Given the risk in the system, even in hindsight, it was a perfectly reasonable strategy.
Finally, it was not 'Dr. Fauci' - it was the same across the Western world. UK and Canada started mandating in July, France in August.