The proper pronouciation is "FEEDTHROUGH".
From
https://www.thefreedictionary.com/feedthrough:"A conductor connecting two circuits on opposite sides of a printed circuit board." (source: American Heritage Dictionary)
"a conductor used to connect two sides of a part, such as a printed circuit board" (source: Collins English Dictionary)
I was raised to call them feedthroughs. Everyone called them feedthroughs. There was precisely zero confusion. Then I got away from hardware for ~10 years at one point in my career, and when I circled back around to being involved in PCB's suddenly there were these things called "vias". I had no idea what they were talking about for a while.
I suspect, but have no evidence, that "via" showed up about the time that CAD and layout programs replaced hand-taping of PCB's. Maybe the software folks were trying to save screen space, or couldn't come up with an abbreviation for "feedthrough" that they liked, or something.
Feedthrough covers every variant:
* All interlayer connections are feedthroughs
* A subset of those involve at least one outside layer and are thus not "buried"
* A subset of those involve both outside layers
* A subset of those also accept a lead of a through-hole component
...and notice the correlation between "feedthrough" and "through-hole component". The word "via" isn't involved at all. They're not "via components".
Through is the proper verb for both the components and the boards into which they install.
Subject settled!