Note, there were many, many different TV and over the years different circutry, all the way up to fully digital signal processing, so any detailed answer would need to be based on what ever TV you're asking about.
My question is about old TV sets which: didn't have a user-adjustable knob for image height,
That would be a very unusual one. They all had knobs to adjust screen height (which essentially is deflection timing between lines)position and width. Usually at the back, some hidden behind a door. Without would be extreme unusual as analogue TV is about analogue components which change over time.
but used some digital components inside (maybe even for the beam deflection control).
Well, there were some (very late, high priced) TV using fully digital image handling which would decode (and possibly store) the signal before creating output.
As I understand, such TVs were calibrated at factory to produce 4:3 image when fed with the actual broadcast signal.
And calibrated at setup plus recalibration every now and then due to agingcomponents.
But what happened if the video source is a computer with more lines and slower frame rate? Did the beam go as usual (retracing more as v-sync would always be late), or were the vertical oscillations slowed down to fit the frequency?
For a real one (analogue), it just displayed, according to its fixed setup, what came. Strictly according to signal frame.
- 'Homing' when a picture starts and
- advancing a line when told so.
That's why those always had two knobs for vertical, one for picture height (line height) and picture position (essentially home position). Plus more for width.
Of course all components would only work within their limits, so while even a 1960s 50 Hz TV might be able to catch a 60 Hz picture(*1), it'll fail at 70 or more.
*1 - Which was in fact my very first journey into TV technology ca. 1972. Shortly after the 'Munich Olympics, when prices for colour TV dramatically dropped, we finally got a colour telly, which meant the old B&W became available to me (*2). Fiddling with the TV I one day found what seemed to be a weak TV signal of a station that shouldn't be there as I already had all 7 stations (4 programs) within reach. So there was a riddle to be solved. After playing with the antenna - and installing second outside, hanging from a rain drain - and even more fiddling with the four knobs on the back of that TV, I was able to get an acceptable picture of a station I never have seen nor expected,showing Flintstones on Sunday at 10 AM, when German TV was at best some super booring church service.
Jay!
AFN TV - we happend to live about 10 km from the Munich McGraw barracks, which also featured a low power TV station to serve a nearby US housing area. So yes, I learned TV by looking out for Hanna-Barbera cartoons.))
*2 - Well, not directly, 'cause TV was already back then bad for kids, but it was move to the upstairs guest room, getting me as regular guest :))